Mathematics of finance MCQS
Simple Interest
Question 1.
₹ 8,000 becomes ₹ 10,000 in two years at simple interest. The amount that will become ₹ 6,875 in 3 years at the same rate of interest is : [1 Mark, Nov. 2006]
(a) ₹ 4,850
(b) ₹ 5,000
(c) ₹ 5,500
(d) ₹ 5,275
Answer:
Tricks
(b) S.I./year = 10000−80002 = ₹ 1000
r = 1000×1008000 = 12.5%
P = Amt Amt at ₹1=68751+0.125×3
= ₹ 5000
∴ (b) is correct.
Question 2.
The rate of simple: interest on a sum of money is 6% p.a. for first 3 years, 8% p.a. for the next five years and 10% p.a. for the period beyond 8 years. If the simple interest accrued by the sum for a period for 10 years is ₹ 1,560. The sum is : [1 Mark, Feb. 2007]
(a) ₹ 1,500
(b) ₹ 12,000
(c) ₹ 3,000
(d) ₹ 5,000
Answer:
(b) is correct.
Single S.I For 1 yrs = (6 × 3 + 8 × 5 + 10 × 2)%
= 78%
Tricks: p = Total S.IS.I on Rs1=15600.78 = ₹ 2000
(b) is correct
Question 3.
A sum of money doubles itself in 10 years. The number of years it would treble itself is : [1 Mark, Feb. 2007]
(a) 25 years
(b) 15 years
(c) 20 years
(d) None.
Answer:
(c) is correct.
Tricks : SEE Type XV (ii) of “Quicker BMLRS book”
t2t1=x2−1x1−1
or t210=3−12−1 or t2 = 20 yrs
(c) is correct
Question 4.
A certain sum of money amounts to ₹ 6,300 in two years and ₹ 7,875 in three years nine months at simple interest. Find the rate of interest per annum : [1 Mark, May 2007]
(a) 20%
(b) 18%
(c) 15%
(d) 10%
Answer:
(a) is correct.
Tricks:
S.I = Arsts for 3.75yrs− Amts for 2yrs(3.75−2)yrs
= ₹ 900
P = 6300 – 2 × 900 = ₹ 4500
r = 900×1004500×1 = 20%
Question 5.
A person borrows ₹ 5,000 for 2 years at 4% p.a. simple interest. He immediately lends to another person at 614% p.a. for 2 years. Find his gain in the transaction per year: [1 Mark, Nov. 2007]
(a) ₹ 112.50
(b) ₹ 125
(c) ₹ 225
(d) ₹ 167.50
Answer:
(a) % Gain = 614% – 4 = 2.25%
S.I for 2 yrs. = 5000 × 2.25% × 2 = ₹ 225
S.I per yr. = 5000 × 2.25% = ₹ 112.50
∴ (a) is correct
Question 6.
Two equal sums of money were lent at simple interest at 11 % p.a. for 3 12 years and 412 years respectively. If the difference in interests for two periods was ₹ 412.50, then each sum is: [1 Mark, Feb. 2008]
(a) ₹ 3,250
(b) ₹ 3,500
(c) ₹ 3,750
(d) ₹ 4,350
Answer:
(C) Tricks : Difference in interest is due to time
∴ rate of interest for the whole
duration = (11 × 4.5 – 11 × 3.5) = 11%
P = Total S.I Interest on ₹1=412.500.11 = 3750
(c) is correct
Question 7.
In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum ? [1 Mark, June 2008]
(a) 114 years
(b) 134 years
(c) 214 years
(d) 234 years
Answer:
(a) is correct
or t = 0.125 × 10 = 1.25yrs
(a) is correct
Question 8.
Find the numbers of years in which a sum doubles itself at the rate of 8% per annum.
(a) 1112
(b) 1212
(c) 912
(d) 1312
Answer:
(b) is correct
Tricks : t = =(x−1)×100r
= (2−1)×1008 = 12.5 yrs
Question 9.
The time by which a sum of money is 8 times of itself if it double itself in 15 years. [1 Mark, June 2009]
(a) 42 years
(b) 43 years
(c) 45 years
(d) 46 years
Answer:
(c) is correct
It is Compound Interest Qts.
Tricks : 2t2 = 815
or 2t2 = (23)15 : t2 =45yrs
Question 10.
What is the rate of simple interest if a sum of money amount ₹ 2,784 in 4 years and ₹ 2,688 in 3 years ? [1 Mark, June 2009]
(a) 1%p.a.
(b) 4%p.a.
(c) 5%p.a.
(d) 8%p.a.
Answer:
(b) is correct
Question 11.
If a simple interest on a sum of money at 6% p.a. for 7 years is equal to twice of simple interest on another sum for 9 years at 5% p.a. The ratio will be: [1 Mark, June 2011]
(a) 2:15
(b) 7:15
(c) 15:7
(d) 1:7
Answer:
(c) is correct
Tricks:- GBC
Question 12.
By mistake a clerk, calculated the simple interest on principal for 5 months at 6.5% p.a. instead of 6 months at 5.5% p.a. If the error in calculation was ₹ 25.40. The original sum of principal was .
(a) ₹ 60,690
(b) ₹ 60,960
(c) ₹ 90,660
(d) ₹ 90,690
Answer:
(b) is correct
P = 25.405.5100×612−6.5100×512
= 25.40×12005.5×6−6.5×5 = ₹ 60, 960
Question 13.
It the Simple Interest on ₹ 1,400 for 3 years is less than the simple interest on ₹ 1,800 for the same period by ₹ 80, then the rate of interest is: [1 Mark, Dec. 2011]
(a) 5.67%
(b) 6.67%
(c) 7.20%
(d) 5.00%
Answer:
(b) is correct.
Tricks: r = 80×100(1800−1400)×3
= 6.67%
Question 14.
The S.I. on a sum of money is 49 of the principal and the No. of years is equal to the rate of interest per annum. Find the rate of interest per annum? [1 Mark, June 2012]
(a) 5%
(b) 20/3%
(c) 22/7%
(d) 6%
Answer:
(b) S.I. = p.r.r100⇒49p. = p.(r10)2
∴ r10=23
r = 203%
Question 15.
Simple interest on ₹ 2,000 for 5 months at 16% p.a. is : [1 Mark, June 2012, Dec. 2012]
(a) ₹ 133.33
(b) ₹ 133.26
(c) ₹ 134.00
(d) ₹ 132.09
Answer:
(a) S.I. = 2000 × 512×16100 = ₹ 133.33
Question 16.
How much investment is required to yield an Annual income of ₹ 420 at 7% p.a. Simple interest. [1 Mark, Dec. 2012]
(a) ₹ 6,000
(b) ₹ 6,420
(c) ₹ 5,580
(d) ₹ 5,000
Answer:
(a) P = 420×1007×1 = ₹ 6000
Calculator Tricks II GBC :
P = 420 ÷ 7% button = ₹ 6000
Question 17.
Mr. X invests ₹ 90,500 in post office at 7.5% p.a. simple interest. While calculating the rate was wrongly taken as 5.7% p.a. The difference in amounts at maturity is t 9,11 A. Find the period for which the sum was invested. [1 Mark, Dec. 2012]
{a) 7 years
(b) 5.8 years
(c) 6 years
(d) 8 years
Answer:
(c) Tricks
t = 9774×10090,500×(7.5−5.7) = 6yrs
Question 18.
If the sum of money when compounded annually become ₹ 1140 in 2 years and ₹ 1710 in 3 years at rate of interest [1 Mark, June 2013]
(a) 30%
(b) 40%
(c) 50%
(d) 60%
Answer:
(c) Interest in 3rd yr = ₹ 1710 – ₹ 1140
= ₹ 570
Tricks Note : For 3rd yr ; it will be like S.I
r = ∴ I×100P.t=570×1001140×1 = 50%
Tricks II Go by choices.
For (c) A = 1140 + 50% (Calculator)
= ₹ 1710
(c) is correct
Question 19.
In what time will a sum of money double itself at 6.25% p.a. at simple interest: [1 Mark, Dec. 2013]
(a) 5 yrs
(b) 8 year
(c) 12 yrs
(d) 16yrs
Answer:
(D) Is correct.
Tricks : See Quicker BMLRS.
Question 20.
What principal will amount to ₹ 370 in 6 years at 8% p.a. at simple interest : [1 Mark, Dec. 2013]
(a) ₹ 210
(b) ₹ 250
(c) ₹ 310
(d) ₹ 350
Answer:
(b) is correct
Tricks: P = =3701+6×0.08 = ₹ 250
(See Quicker BMLRS)
Calculator Tricks GBC
(b) Amt = 250 + (6 x 8)% button press = 370
Question 21.
If a sum triples in 15 yrs at Simple rate of interest then the rate of interest per annum will be: [1 Mark, June 2014]
(a) 13.0%
(b) 13.3%
(c) 13.5%
(d) 18%
Answer:
(b) is correct
Tricks r = (3−1)×1001×15 = 13.3%
Calculator Tricks GBC
(b) r = 15 × 13.333% = 200%
A = 1 + 200% (button) = 3
(b) is correct
Question 22.
A certain sum of money was invested at simple rate of interest for three years. If it was invested at 7% higher, the interest have been ₹ 882 more, then sum has been invested at that rate was: [1 Mark, Dec. 2014]
(a) ₹ 12,600
(b) ₹ 6,800
(c) ₹ 4,200
(d) ₹ 2,800
Answer:
(c) is correct
S.I = ₹ 882 for r = 7%
t = 3 years.
P = I×100rt=882×1007×3 = ₹ 4200
Calculator Tricks: GBC
Question 23.
A sum of money will be doubled itself in 8 years at S.I. In how many years the sum will be tripled itself ? [1 Mark, June 2015]
(a) 20 years
(b) 12 years
(c) 16 years
(d) None
Answer:
(c) is correct.
Tricks: t28=3−12−1
t2 = 16yrs.
Question 24.
A sum of 44,000 is divided into 3 parts such that the corresponding interest earned after 2 years, 3 years and 6 years may be equal at the rate of simple interest are 6% p.a. 8% p.a. & 6% p.a., respectively. Then the smallest part of the sum will be. [1 Mark, June 2015]
(a) ₹ 4,000
(b) ₹ 8,000
(c) ₹ 10,000
(d) ₹ 12,000
Answer:
(b) is correct.
= 6:3:2
So, Smallest principal = 440006+3+2 × 2 = ₹ 8000
Question 25.
No. of years a sum of money becomes 4 times itself at 12% p.a. at simple interest: [1 Mark, Dec. 2015]
(a) 20
(b) 21
(c) 25
(d) 30
Answer:
(c) is correct
Tricks: t = (4−1)×1001×12 = 25 yrs
Question 26.
If a person lends ₹ 6,000 for 4 years and ₹ 8,000 for 3 years at S.I. The total interest earned is ₹ 2400 then the rate of interest is: [1 Mark, Dec. 2016]
(a) 5%
(b) 6%
(c) 1%
(d) 8%
Answer:
(a) is correct.
Tricks: Go by choices.
For (a);
Total SI = 6000 × 4. × 5% + 8000 × 3 × 5%
= ₹ 2400
So, (a) is correct.
Question 27.
In simple interest, a certain sum becomes ₹ 97,920 in 3 years, and ₹ 1,15,200 in 5 years, then the rate of interest is: [1 Mark, June 2018]
(a) 10%
(b) 11.2%
(c) 12%
(d) 13.6%
Answer:
(c)
Tricks :
S.I p.a = 1,15,200−97,9205−3
= ₹ 8640
Principal = 97,920 – 3 yrs interest = 97,920 – 3 x 8640 = ₹ 72,000
r = 8640×10072000 = 12%
Calculator Tricks:
Amounts = 72000 + (12 × 3 = 36) % button = ₹ 97,920 (True)
So, option (C) is correct.
Question 28.
A person borrows Rs. 5,000 for 2 years at 4% per annual simple interest. He immediately lends to another person at 6 – % . Per annual for 2 years find his gain in the transaction . [1 Mark, May 2018]
(a) Rs. 112.50
(b) Rs. 225
(c) Rs. 125
(d) Rs. 107.50
Answer:
(b)
Interest Gain = (614 – 4) = 214 = 2.25%
So, Interest Gain
= 5000×2×2.25100 = Rs. 225
Question 29.
A certain money doubles itself in 10 years when deposited on simple interest. It would triple itself in: [1 Mark, Nov. 2018]
(a) 30 years
(b) 20 years
(c) 25 years
(d) 15 years
Answer:
(b)
Tricks : See Simple Interest (Quicker BMLRS)
t2t1=x2−1x1−1
⇒ t210=3−12−1 ⇒ t2 = 20 yrs.
Question 30.
A certain sum of money Q was deposited for 5 year and 4 months at 4.5% simple interest and amounted to ₹ 248, then the value of Q is: [1 Mark, Nov. 2018]
(a) ₹ 240
(b) ₹ 200
(c) ₹ 220
(d) ₹ 210
Answer:
(b)
t = 5 yrs 4 months = 5 + 412=163 yrs
Tricks : GBC
Rates for 5 yrs 4 Months = 5 × 4.5 %+ one third of 4.5% = 24%
Note : 4 months means one third of one year, so rate for 4 months = one third of one year interest rate.
(b) Amounts = 200 + 24% = 248 (True)
So, (b) is correct.
Question 31.
The certain sum of money became Rs. 692 in 2 yrs. and Rs. 800 in 5 yrs. then the principle amount is: [1 Mark, June 2019]
(a) Rs. 520
(b) Rs. 620
(c) Rs. 720
(d) Rs. 820
Answer:
(b)
Tricks:- If a certain sum of money becomes A1 in t1 years and A2 in t2 years then S.I. per annum = A2−A1t2−t1
S.I. p.a = 800−6925−2 = Rs. 36.
Principal = A – Interest
= 692 – Interest of 2 yrs.
= 692 – 2 × 36 = Rs. 620.
(b) is correct.
Question 32.
A sum of money amount to Rs. 6,200 in 2 years and Rs. 7,400 in 3 years as per S.I. then the principal is: [1 Mark, June 2019]
(a) Rs. 3,000
(b) Rs. 3,500
(c) Rs. 3,800
(d) None
Answer:
(c)
Tricks:- S.I. p.a = 7400−62003−2
= Rs. 1200.
Principal = 6200 – 2 × 1200
= Rs. 3800.
Question 33.
P = Rs. 5,000; R = 15%; T = 412 using I = PTR 100 then I will be I = Prt 100 [1 Mark, June 2019]
(a) Rs. 3,375
(b) Rs. 3,300
(c) Rs. 3,735
(d) None
Answer:
(a)
I = 5000×15×4.5100 = 3375
[Use Calculator ; Never Write]
Question 34.
In simple interest if the principal is Rs. 2,000 and the rate and time are the roots of the equation x2 – 11x – 30 = 0 then simple interest is : [1 Mark, June 2019]
(a) Rs. 500
(b) Rs. 600
(c) Rs. 700
(d) Rs. 800
Answer:
(b)
∵ x2 – 11x + 30 = 0
or x2 – 5x – 6x + 30 = 0
or x(x – 5) – 6(x – 5)= 0
or (x – 5) (x – 6) = 0
∴ x = 5 ; 6
If r = 5% then t = 6 yrs.
S.I = Undefined control sequence \operatorname
= Rs. 600.
(b) is correct.
COMPOUND INTEREST
Question 1.
The difference between the simple and compound interest on a certain sum for 3 year at 5% p.a. is 228.75. The compound interest on the sum for 2 years at 5% p.a. is: [1 Mark, Nov. 2006]
(a) 3,175
(b) 3,075
(c) 3,275
(d) 2,975
Answer:
Tricks
P = Difference ×(100)3r2(300+r) [For 3 years only]
= 228.75×(100)35×5(300+5) = ₹ 30,000
A = 30000 + 5 % + 5% buttons = ₹ 33075
∴ C.I = A – P = ₹ 33075 – 30000
= ₹ 3,075
(b) is Correct
Question 2.
In what time will ₹ 3,90,625 amount to ₹ 4,56,976 at 8% per annum, when the interest is compounded semi-annually ? [Given: (1.04) = 1.16986] [1 Mark, Feb. 2007]
(a) 2 years
(b) 4 years
(c) 5 years
(d) 1 years
Answer:
(a)
A = P(1 + r100m)mt
4,56,9763,90,625=(1+8200)2t
or 1.16985856 = (1.04)2t
or 1.16966 = (1.04)2t
or (1.04)4 = (1.04)2t
∴ 2t = 4 ∴ t = 2 years
(a) is correct
Question 3.
How long will ₹ 12,000 take to amount to ₹ 14,000 at 5% p.a. converted quarterly? [Given: (1.0125)124 = 1.1666] [1 Mark, May 2007]
(a) 3 years
(b) 3.1 years
(c) 13.5 years
(d) 12.4 years.
Answer:
(b) Ap=(1+5400)4t
or 1400012000 = (1.0125)4t
or 1.16666…………… (1.0125)4t
or (1.0125)12.4 = (1.0125)4t
[Note Always use values given in question]
or 4t= 12.4 ∴ t = 3.1yrs.
∴ (b) is correct
Tricks See Type – VII. (Quicker BMLRS)
Question 4.
If ₹ 1,000 be invested at interest rate of 5% and the interest be added to the principal every 10 years, then the number of years in which it will amount to ₹ 2,000 is : [1 Mark, Aug. 2007]
(a) 1623years
(b) 110 years
(c) 16 years
(d) 623 years
Answer: A IS CORRECT
Question 5.
The annual birth and death rates per 1000 are 39.4 and 19.4 respectively. The number of years in which the population will be doubled assuming there is no immigration or emigration is : [1 Mark, Aug. 2007]
(a) 35 years
(b) 30 years
(c) 25 years
(d) None of these
Answer:
Tricks See Type VIII
Question 6.
The effective rate equivalent to nominal rate of 6% compounded monthly is:
(a) 6.05
(b) 6.16
(c) 6.25
Answer:
(b)
option (b) is Correct.
Tricks See Type III
Question 7.
A person deposited 15,000 in a bank. The deposit was left to accumulate at 6% compounded quarterly for the first five years and at 8% compounded semiannually for the next eight years. The compound amount at the end of 13 years is : [1 Mark, Nov. 2007]
(a) ₹ 12621.50
(b) ₹ 12613.10
(c) ₹ 13613.10
(d) None.
Answer:
Calculator Tricks See Type X
A = 5000(1 + 6400)5×4 (1 + 8800)8×2
₹ 12613.17 = ₹ 12610.00 (approx)
(b) is correct.
Question 8.
Anshul’s father wishes to have ₹ 75,000 in a bank account when his first college expenses begin. Howmuchamount his father should depositnowat6.5%compounded annually if Anshul is to start college in 8 years hence from now? [1 Mark, Feb. 2008]
(a) ₹ 45,320
(b) ₹ 46,360
(c) ₹ 55,360
(d) ₹ 48,360.
Answer:
(a) Calculator Tricks
(a) is correct
Question 9.
The difference between compound interest and simple interest on a certain sum for 2 years @ 10% p.a. is ₹ 10. Find the sum:
(a) ₹ 1,010
(b) ₹ 1,095
(c) ₹ 1,000
(d) ₹ 990
Answer:
(c) Tricks
(c) is correct
Calculator Tricks For 2 years. P = 10 ÷ 10% ÷ 10% button = ₹ 1000.
Question 10.
A machine worth ₹ 4,90,740 is depreciated at 15% on its opening value each year. When its value would reduce to ₹ 2,00,000 : [1 Mark, June 2008]
(a) 5 years 6 months
(b) 5 years 7 months
(c) 5 years 5 months
(d) None
Answer:
(a) is correct
Tricks :-See Type -VI (Quicker BMLRS)
t = log(2,00,000/4,90,740)log(1−15/100)
= 5.5 years (approx.)
= 5 yrs. 6 months
Question 11.
If the difference between simple interest and compound interest is ₹ 11 at the rate of 10% for two years, then find the sum: [1 Mark, Dec. 2008]
(a) ₹ 1,200
(b) ₹ 1,100
(c) ₹ 1,000
(d) None of these
Answer:
(b) is correct
Tricks P = = Difference ×(100)2( rate )2
= 11×(100)2(10)2 = ₹ 1100
Calculator Tricks P = 11 + 10% = 10% button = ₹ 1100
Question 12.
In how many years, a sum will become double at 5% p.a. compound interest. [1 Mark, June 2009]
(a) 14.0 years
(b) 14.1 years
(c) 14.2 years
(d) 14.3 years
Answer:
(c) is correct
Tricks t = log(A/P)melog(1+r/100m)
= =log(A/P)melog(1+r/100m) = 14.2yrs (approx)
See Quicker BMLRS.
Question 13.
Asum amount to ₹ 1331 at a principal of ₹ 1,000 at 10 % compounded annually. Find the time.
(a) 3.31 years
(b) 4 years
(c) 3 years
(d) 2 years
[1 Mark, June 2009]
Answer:
(c) is correct
Tricks Go by choices
For (c); A = 1000(1 + 10100)3 = ₹ 1331
So; t = 3 yrs.
Calculator Tricks: GBC
(c) A = 1000 + 10% + 10% + 10% button = ₹ 1,331
Question 14.
In how many years, a sum of ₹ 1000 compounded annually @10% will amount to 1331? [1 Mark, Dec. 2009]
(a) 6 years
(b) 5 years
(c) 4 years
(d) 3 years
Answer:
See the above QTS. (13).
Question 15.
The compound interest for a certain sum @ 5% p.a. for first years is ?25. The S-I for the same money @ 5% p.a. for 2 years will be. [1 Mark, Dec. 2009]
(a) ₹ 40
(b) ₹ 50
(c) ₹ 60
(d) ₹ 70
Answer:
(b) is correct Tricks
S.I For 1st yrs. = C. I for 1st yrs. = ₹ 25 S.I
For 2 yrs. For same ‘p’ = 2 × 25 = ₹ 50
Question 16.
At what % rate of compound interest corresponding (C.I) will a sum of money became 16 times in four years, if interest is being calculated compounding annually:
(a) r = 100%
(b) r = 10%
(c) r = 200%
(d) r = 20%
Answer:
(a) is correct
Tricks Go by choices
For (a) Let P = 1; A = 1(1 + 100100)4 = (2)4 = 16
(a) is correct
Question 17.
If the simple interest on a sum of money at 12% p.a. for two years is ₹ 3,600. The compound interest on the same sum for two years at the same rate is: [1 Mark, June 2010]
(a) ₹ 3,816
(b) ₹ 3,806
(c) ₹ 3,861
(d) ₹ 3,860
Answer:
(a) is correct
P = 3600×10012×2 = ₹ 15000
∴ c.i = 15000(1 + 12100)2 – 15000 = ₹ 3816
Tricks:-
CI for 1st yr. = SI for 1st year = 3600 ÷ 2 = ₹ 1800
CI for 2nd year = 1800 + 1800 × 12% = ₹ 2016
C.I for 2 years = 1800 + 2016 = ₹ 3816.
Question 18.
The effective annual rate of interest corresponding to nominal rate 6% p.a. payable half yearly is: [1 Mark, Dec. 2010]
(a) 6.06%
(b) 6.07%
(c) 6.08%
(d) 6.09%
Answer:
(d) is correct
re = [(1 + 6200)2 – 1]
Question 19.
The cost of Machinery, is ₹ 1,25,000/- If its useful life is estimated to be 20 years and the rate of depreciation of its cost is 10% p.a., then the scrap value of the
Machinery is (given that(o.9)20 = 0.1215)
(a) 15,187
(b) 15,400
(c) 15,300
(d) 15,250
Answer:
(a) is correct
S(Scrap Value) = P(1−d100)t
where P = Principal;
d = rate of depreciation
∴ S = 1,25,000(1−10100)20
= ₹ 15,187.50
Question 20.
Mr. X invests ‘P’ amount at Simple Interest rate 10% and Mr. Y invests ‘Q’ amount at Compound Interest rate 5% compounded annually. At the end of two years both get the same amount of interest, then the relation between two amounts P and Q is given by:
(a) p = 41Q80
(b) p = 41Q40
(c) p = 41Q100
(d) p = 41Q200
Answer:
(a) is correct
S.I = P.10×2100=P5
C.I = Q[(1+5100)2−1]
= 0.1025. Q
From Question
S.I = C.I
Question 21.
If the difference of S.I and C.I is ₹ 72 at 12% for 2 years. Calculate the amount. [1 Mark, June 2011]
(a) 8,000
(b) 6,000
(c) 5,000
(d) 7,750
Answer:
(c) is correct
Tricks: P = (C.I−S.I)×(100)2r2
= 72×100×10012×12 = ₹ 5000
Calculator Tricks:
P = 72 ÷ 12% ÷ 12% = 5000
Question 22.
Nominal rate of interest is 9.9% p.a. If interest is Compounded monthly, What will be the effective rate of interest
(Given (40334000)12 = 1.1036 (approx))? [1 Mark, Dec. 2011, June 2012]
(a) 10.36%
(b) 9.36%
(c) 11.36%
(d) 9.9%
Answer:
(a) is correct.
Tricks:
re = [(1+9.91200)12 – 1] × 100
= 10.36%
Question 23.
The difference between Cl and SI on a certain sum of money for 2 years at 4% per annum is ? 1. The sum is: [1 Mark, June 2013]
(a) 625
(b) 630
(c) 640
(d) 635
Answer:
(a) is correct
Tricks For 2 yrs
Sum of Money = Diff. (100)2r2
= 1×(100)242 = ₹ 625
Calculator Tricks:- P = 1 ÷ 4% = 4% button = ₹ 625.
Question 24.
If the sum of money when compounded annually become 1140 in 2 years and 1710 in 3 years at rate of interest: [1 Mark, June 2013]
(a) 30%
(b) 40%
(c) 50%
(d) 60%
Answer:
(c) is correct.
Interest in 3rd yr. = ₹ 1710 – ₹ 1140 = ₹ 570 ;
Tricks Note For 3rd yr; it will be like S.I ,
r = ∴ 1×100Pt=570×1001140×1 = 50%
Tricks II Go by choices.
For (c) A = 1140 + 50% (Calculator)
= ₹ 1710
∴ (c) is correct
Question 25.
The difference between and C.I & S.I at 7% p.a. for 2 years is ₹ 29.4 then principal is: [1 Mark, Dec. 2013]
(a) ₹ 5,000
(b) ₹ 5,5000
(c) ₹ 6,000
(d) ₹ 6,500
Answer:
(c) is correct
Tricks P = = Difference ×(100)2r2
= 29.4×(100)2(7)2 = ₹ 6000
(See Quicker BMLRS)
Calculator Tricks P = 29.4 ÷ 7% + 1% button = ₹ 6000
Question 26.
The Partners A & B together lent ₹ 3903 at 4% p.a. interest compounded annually. After a spam of 7 years, A gets the same amount as B gets after 9 years. The share of A in the sum of ₹ 3903/- would have been [1 Mark, June 2014]
(a) ₹ 1875
(b) ₹ 2280
(c) ₹ 2028
(d) ₹ 2820
Answer:
(c) is correct
Tricks:- GBC
Question 27.
A certain sum of money double itself in 4 years at C.I. In how many years it will become 32 times to itself: [2014-Dec.]
(a) 15 years
(b) 24 years
(c) 20 years
(d) None
Answer:
(c) is correct
Tricks:- 2t2 – 324
= 2t2 = (25)4 = 220
= t2 = 20
Question 28.
On a certain sum rate of interest @ 10% p.a., S.I= ₹ 90 Term = 2 year, Find Compound interest for the same : [1 Mark, Dec. 2015]
(a) ₹ 544.5
(6) ₹ 94.5
(c) ₹ 450
(d) ₹ 18
Answer:
(b) is correct
S.I ,p.a = 902 = ₹ 45
Tricks: Compound interest
= 45 + (45 + 10%) = ₹ 94.5
Question 29.
If an amount is kept at simple interest, it earns ₹ 600 in first 2 years but when kept at Compound interest it earns at interest of ₹ 660 for the same period; then the rate of interest and principle amount respectively are: [1 Mark, June 2016]
(a) 20%; ₹ 1200
(b) 10%; ₹ 1200
(c) 20%; ₹ 1500
(d) 10%; ₹ 1500
Answer:
(c)
Tricks:- Go by choices
(c) S.I = 1500×2×20100 = ₹ 600(True)
C.I = 1500[(1+20100)2 – 1] = ₹ 660 (also True)
(c) is correct
Question 30.
Mr. X bought an electronic item for ₹ 1000. What would be the future value of the same item after two years, if the value is compounded semi-annually at the rate of 22% per annum ?
(a) ₹ 1488.40
(b) ₹ 1518.07
(c) ₹ 2008.07
(d) ₹ 2200.00
Answer:
(b) is correct
FV = P (1 + i)n
= ₹ 1518.07 (approx.)
Question 31.
The difference between the simple interest and compound interest on a certain sum of money invested for 2 years at 5% p.a. is ₹ 30. Then the sum = [1 Mark, Dec. 2016]
(a) 10,000
(b) 12,00
(c) 13,000
(d) None
Answer:
(b) Calculator Tricks:
P = 30 ÷ 5% ÷ 5% button = ₹ 12,000
Question 32.
A sum of money amounts to ₹ 7803 for one year at the rate of 4% compounded semi-annually then the sum invested is: [1 Mark, Dec. 2016]
(a) 7,000
(b) 7,500
(c) 7,750
(d) 8,000
Answer:
(b)
Calculator Tricks:
P = (4 ÷ 200 + 1)÷ = button 2 times × 7803 = button = ₹ 7500
Tricks : (b) (GBC) → A = 7500 + 2% + 2% button = 7803.
Question 33.
The difference between simple and compound interest on a sum of ? 10000 for 4 years at the rate of interest 10% per annum is: [1 Mark, 2017 June]
(a) 650
(b) 640
(c) 641
(d) 600
Answer:
C.I – S.I
= [10,000(1+10100)4 – 10,000] – [10,000×10×4100]
= 4641 – 4000 = ₹ 641
option (c) is correct. [Note: Do by Calculator]
Question 34.
If the compound interest on a sum for two year at the rate 5% p.a. is ₹ 512.50, then the principal is: [1 Mark, Dec. 2017]
(a) 4,000
(b) 3,000
(c) 5,000
(d) None of these
Answer:
(c)
Tricks:- GBC
Amount = 5000 + 5% + 5% button
= 5512.50.
C.I = 5512.50 – 5000 = ₹ 512.50.
Question 35.
Find effective rate of interest corresponding to the nominal rate of interest 7% compounded monthly is : [1 Mark, Dec. 2017]
(a) 7.26%
(b) 7.22%
(c) 7.02%
(d) 7.20%
Answer:
(b)
re = [(1+71200)12 – 1] × 100%
= 7. 229 % = 7.22 %
Question 36.
In compound interest, if the amount is 9 times to its principle in two years then the rate of interest is ? [1 Mark, June 2018]
(a) 300%
(b) 200%
(c) 150%
(d) 100%
Answer:
(b), Given,
Tricks : – 1 + 200 % + 200 % = 9
So, (b) is correct.
Question 37.
If difference between Compound Interest and Simple Interest for 3 years is ₹ 912 at the rate 4 % p.a., the principal is: [1 Mark, June 2018]
(a) ₹ 1,87,500
(b) ₹ 1,87,000
(c) ₹ 1,87,550
(d) ₹ 1,85,700
Answer:
(a)
Tricks
P = 912 ÷ 4% ÷ 4% ÷ (300 + 4)%
= ₹ 1,87,500
See QUICKER BMLRS
Question 38.
If Rs. 1,000 be invested at interest at interest rate of 5% and the interest be added to the principal every 10 years, than the number of years in which it will amount to Rs. 2,000 is : [1 Mark, May 2018]
(a) 1623 years
(b) 614
(c) 16 years
(d) 623
Answer:
(a)
∵ Interest is added to the principal every 10 years. So, within 10 years ; simple interest will apply.
So, Amount after 10 yrs.
= 1000 + 1000 × 10×5100
= Rs. 1500.
Total amount = Rs. 2000
Extra Interest needed = 2000 – 1500
= Rs. 500.
Time = 500×1001500×5=203
= 623 yrs.
So; Total time = 10 + 623
= 1623 yrs
Question 39.
If an amount is kept at S.I. it earns an interest of Rs. 600 in first two years but when kept at compound interest it earns an interest of Rs. 660 for the same period, then the rate of interest and principal amount respectively are : [1 Mark, May 2018]
(a) 20%., Rs. 1,200
(b) 20%, Rs. 1,500
(c) 10%, Rs. 1,200
(d) 10%., Rs. 1,500
Answer:
(b)
Tricks:- Go by choices (GBC)
(a) S.I = 1200×2×20100 = 480
So; (a) is false.
(b) S.I = 1500×2×20100 = Rs. 600
So; (b) is True.
C.I = (-1500 + 20% + 20%) (button)
= 660
Question 40.
If ₹ 10,000 is invested at 8% per year compound quarterly, then the value of the investment after 2 years is [Given (1+ 0.2)8 = 1.171659]
(a) ₹ 10,716.59
(b) ₹ 11,716.59
(c) ₹ 117.1659
(d) None of these
Answer:
(b)
FV = 100000(1 + 8400)2×4
= ₹ 11716.59
Calculator Tricks: See Quicker BMLRS
Chapter: Compound Interest
Question 41.
A bank pays 10% rate of interest, interest being calculated half yearly. A sum of ₹ 400 is deposited in the bank. The amount at the end of 1 years will be: [1 Mark, Nov. 2018]
(a) ₹ 439
(b) ₹ 440
(c) ₹ 442
(d) ₹ 441
Answer:
(d)
FV = 400(1+10200)2 = 441
Calculator Tricks :
FV = 8000 + 5 % + 5 % + 5 % buttons = ₹ 9261
Question 43.
If in two years time a principal of ₹ 100 amounts to ₹ 121 when the interest at the rate of r % is compounded annually, then the value of r will be
(a) 14
(b) 10.5
(c) 15
(d) 10
Answer:
(d)
Details:
II Calculator Tricks
FV = 100+ 10% + 10% buttons = 121 (True)
Question 44.
The effective rate of interest for one year deposit corresponding to a nominal 7% rate of interest per annum convertible quarterly is: [1 Mark, Nov. 2018]
(a) 7%
(b) 7.4%
(c) 7.5%
(d) 7.18%
Answer:
(d)
re = [(1+7400)4 – 1] x 100 = 7.18%
Question 45.
How much will ₹ 25,000 amount to in 2 years at compound interest if the rates for the successive years are 4% and 5% per year: [1 Mark, Nov. 2018]
(a) ₹ 27,000
(b) ₹ 27,300
(c) ₹ 27,500
(d) ₹ 27,900
Answer:
(b)
FV = 25000(1+4100)×(1+5100)
= ₹ 27,300/-
Calculator Tricks:- 25000 + 4% + 5% buttons
= ₹ 27,300/-
Question 46.
₹ 8,000/- at 10% per annum interest compounded half yearly will become at the end of one year: [1 Mark, Nov. 2018]
(a) ₹ 8,800
(b) ₹ 8,900
(c) ₹ 8820
(d) ₹ 9,600
Answer:
(c)
FV = 8000(1+10200)2 = ₹ 8,820
Calculator Tricks
FV = 8000 + 5 % + 5% buttons = 8820
Question 47.
The value of furniture depreciates by 10% a year, if the present value of the furniture in an office is ₹ 21870, calculate the value of furniture 3 years ago: [1 Mark, Nov. 2018]
(a) ₹ 30,000
(b) ₹ 40,000
(c) ₹ 35,000
(d) ₹ 50,000
Answer:
(a)
Calculator TricksGBC
(a) 30000 – 10% – 10% – 10% button = 21870.
Details Method
21870 = P(1+10100)3
P = 21870(0.9)3 = ₹ 30,000
Question 48.
If compound interest on a sum for 2 years at 4% per annum is ₹ 102, then the simple interest on the same period at the same rate will be: [1 Mark, Nov. 2018]
(a) ₹ 90
(b) ₹ 100
(c) ₹ 101
(d) ₹ 93
Answer:
(b)
Tricks Go by choices
For option (b)
S.I. for 2 years = ₹ 100
S.I. for 1 years = ₹ 50
S.I. of 1st yr. = C.I. of 1st yr. = ₹ 50
C.I. for 2nd yr. = 50 + 4% = ₹ 52
Total C.I. for 2 yrs = 50 + 52 = ₹ 102 (True)
Option (b) is correct
Question 49.
If the difference between the compound interest compounded annually and simple interest on a certain amount at 10% per annum for two years is ₹ 372, then the principal amount is: [1 Mark, Nov. 2018]
(a) ₹ 37,000
(b) ₹ 37,200
(c) ₹ 37,500
(d) None of the above
Answer:
(b)
Tricks
P = 372 + 10% ÷ 10% = ₹ 37,200
Question 50.
What is the net present value of piece of property which would be valued at ₹ 2 lakh at the end of 2 years? (Annual rate of increase = 5%): [1 Mark, Nov. 2018]
(a) ₹ 2.00 lakh
(b) ₹ 1.81 lakh
(c) 2.01 lakh
(d) None of the above
Answer:
(b)
NPV = 2(1+5100)−2 = 1.81 lakh (approx)
Question 51.
A sum was invested for 3 years as per C.I. and the rate of interest for first year is 9%, 2nd year is 6% and 3rd year is 3% p.a. respectively. Find the sum if the amount in three years is Rs. 550 ? [1 Mark, June 2019]
(a) Rs. 250
(b) Rs. 300
(c). Rs. 462.16
(d) Rs. 350
Answer:
Question 52.
The effective rate of interest does not depend upon
(a) Amount of Principal
(b) Amount of Interest
(c) Number of Conversion Periods
(d) None of these
Answer:
(a) is correct
Question 53.
If p. i2 = 96, and R = 8% compounded annually then P =
(a) Rs. 14,000
(b) Rs. 15,000
(c) Rs. 16,000
(d) Rs. 17,000
Answer:
(b)
Tricks Given , p. i2 = 96
Means interest of two periods (yrs. here) is 96.
So; GBC (Calculator Tricks)
(a) I = 14000 × 8% × 8%
= 89.6 ≠ 96
So; (a) is False.
(b) Type 15000×8% × 8% button
We get 96.
So; (b) is correct.
Tricks II
P = 968% ÷ 8% buttons.
= Rs. 15,00
Annuity
Question 1.
Mr. X Invests ₹ 10,000 every year starting from today for next 10 years suppose: interest rate is 8% per annum compounded annually. Calculate future value of the annuity: (Given that (1 + 0.08)10 = 2.15892500] [1 Mark, Nov. 2006]
(a) ₹ 156454.88
(b) ₹ 144865.625
(c) ₹ 156554.88
(d) None of these
Answer:
(a) It is Annuity Due Question
A = FV = R[{(1+i)n+1−1r} × 100m – 1]
= 10,000[(1+0.08)10+1−18 × 100 – 1]
= ₹ 1,56,454.88. [ See Type-V ]
(a) is correct
Question 2.
The present value of an annuity of ₹ 3,000 for 15 years at 4.5% p.a. C.I. is: [Given that (1.045)15 = 1.935282]. [1 Mark, Nov. 2006]
(a) ₹ 23,809.67
(b) ₹ 32,218.67
(c) ₹ 32,908.67
(d) None of these
Answer:
PV = R[1−(1+1)−ni]
= 3000[1−(1.045)−150.045]
Tricks = ₹ 32,218.67
[See Calculator Tricks in Type III]
Question 3.
A machine can be purchased for ₹ 50,000. Machine will contribute ₹ 12,000 per year for the next five years. Assume borrowing cost is 10% per annum. Determine whether machine should be purchased or not: [1 Mark, Feb. 2007]
(a) Should be purchased
(b) Should not be purchased
(c) Can’t say about purchase
(d) None of the above
Answer:
(b) PV = R[1−(1+i)−ni]
PV = 12000[1−(1.10)−50.10]
= ₹ 45,489.44
But it costs ₹ 50, 000
It should not be purchased
(b) is correct
Question 4.
How much amount is required to be invested every year so as to accumulate ₹ 3,00,000 at the end of 10 years, if interest is compounded annually at 10 % ? [Give (1.1)10 = 2.5937] [1 Mark, Feb. 2007]
(a) ₹ 18,823.65
(b) ₹ 18,828.65
(c) ₹ 18,832.65
(d) ₹ 18,882.65
Answer:
(a) is correct
Question 5.
A company is considering proposal of purchasing a machine either by making full payment of ₹ 4,000 or by leasing it for four years at an annual rate of ₹ 1,250. Which course of action is preferable, if the company can borrow money at 14% compounded annually ? [Given: (1.14) = 1.68896] [1 Mark, May 2007]
(a) Leasing is preferable
(b) Should be purchased
(c) No difference
(d) None of these
Answer:
(a) ₹ 4000 = Present value
It is less than real cost price.
Leasing is better
(a) is correct
Tricks : See Quicker BMLRS for CA-Foundation.
Question 6.
Vipul purchases a car for ₹ 5,50,000. He gets a loan of ₹ 5,00,000 at 15% p.a. from a Bank and balance ₹ 50,000 he pays at the time of purchase. He has to pay the whole amount of loan in 12 equal monthly instalments with interest starting from the end of the first month. The money he has to pay at the end of every month is : [Given (1.0125)12 = 1.16075452] [1 Mark, May 2007]
(a) ₹ 45,130.43
(b) ₹ 45,230.43
(c) ₹ 45,330.43
(d) None of these
Answer:
Loan Value = ₹ 5,00,000 = PV
R = Instalment value = ?
PV = R[1−(1+i)−ni]
5,00,000 = R[1−(1+151200)−12i]
R = 45,130.43.
Tricks : [See Page 9.3 Type IV]
Question 7.
A company establishes a sinking fund to provide for the payment of ₹ 2,00,000 debt maturing in 20 years. Contributions to the fund are to be made at the end of every year. Find the amount of each annual deposit if interest is 5% per annum : [1 Mark, Aug. 2007]
(a) ₹ 6,142
(b) ₹ 6,049
(c) ₹ 6,052
(d) 6,159
Answer:
A = ₹ 200,000
200,000 = R[(1+5/100)20−15×100]
or R = 2,00,000×5[(1.05)20−1)]×100
= ₹ 6049 (Approx)
Tricks : [See Page 9.5 Type IX]
Question 8.
Raja aged 40 wishes his wife Rani to have ₹ 40 lakhs at his death. If his expectation of life is another 30 years and he starts making equal annual investments commencing now at 3% compound interest p.a. How much should he invest annually? [1 Mark, Nov. 2007]
(a) ₹ 84,077
(b) ₹ 81,628
(c) ₹ 84,449
(d) ₹ 84,
Answer:
(b) is correct.
Calculator Tricks : [See Type IX]
Question 9.
A company may obtain a machine either by leasing it for 5 years (useful life) at an annual rent of ₹ 2,000 or by purchasing the machine for ₹ 8,100. If the company can borrow money at 18% per annum, which alternative is preferable? [1 Mark, Feb. 2008]
(a) Leasing
(b) Purchasing
(c) Can’t say
(d) None of these
Answer:
(a) PV = ₹ 8100 It is an ordinary Annuity
PV = 2000[1−(1+8100)−518×100]
= ₹ 6254.34
It is less than ₹ 8100.
(a) is correct
Question 10.
A sinking fund is created for redeeming debentures worth ₹ 5 lacs at the end of 25 years. How much provision needs to be made out of profits each year provided sinking fund investments can earn interest at 4% p.a.?
Answer:
(a) is correct
Tricks: ₹ 5,00,000 = R[(1.04)25−10.04]
∴ R= 12006.00 approx
Question 11.
Future value of an ordinary annuity : [1 Mark, Dec. 2008]
Answer:
(a) is correct.
It is Formulae.
Question 12.
Paul borrowers ₹ 20,000 on condition to repay it with compound interest at 5% p.a. in annual instalment of ₹ 2,000 each. Find the number of years in which the debt would be paid off. [1 Mark, June 2009]
(a) 10 years
(b) 12 years
(c) 14 years
(d) 15years
Answer:
(d) is correct
or 0.5 – 1 = (1.05)-t
or 0.5 – 1 = -(1.05)-t
or (1.05)t = 10.5 = 2
or t = log2log(1.05) = 15 yrs. approx
Tricks : Go by choices
Question 13.
Find the present value of an annuity of ₹ 1,000 payable at the end of each year for 10 years. If rate of interest is 6% compounding per annum. (given (1.06)-10 = 0.5584): [1 Mark, June 2010]
(a) ₹ 7,360
(b) ₹ 8,360
(c) ₹ 12,000
(d) None of these.
Answer:
(a) is correct
PV = 1000[1−(1.06)−100.06]
= ₹ 7360 (a) is correct.
Question 14.
The future value of an annuity of ₹ 5,000 is made annually for 8 years at interest rate of 9% compounded annually
[Given that (1.09)8 =1.99256 ________. [1 Mark, Dec. 2010]
(a) ₹ 55,142.22
(b) ₹ 65,142.22
(c) ₹ 65,532.22
(d) ₹ 57,425.22
Answer:
(a) is correct
FV = 5000[(1.09)8−10.09] = 55,142.22
(a) is correct
Question 15.
How much amount is required to be invested every year as to accumulate ₹ 6,00,000 at the end of 10th year, if interest is compounded annually at 10% rate of interest? [1 Mark, June 2014]
(a) ₹ 37,467
(b) ₹ 37,476
(c) ₹ 37,647
(d) ₹ 37,674
Answer:
(c) is correct
Let amount invested annually = R
R = 6,00,000⎡⎣⎢(1+1100)10−110×100⎤⎦⎥
= ₹ 37,647 (approx)
Note : See Quicker BMLRS.
Question 16.
The future value of an annuity of ₹ 1,000 made annually for 5 years at the rate of interest 14% compound annually is: [1 Mark, Dec. 2014]
(a) ₹ 5610
(b) ₹ 6610
(c) ₹ 6160
(d) ₹ 5160
Answer:
(b) FV = 1000[(1+14100)5−114×100]
= ₹ 6610.104 = ₹ 6610
Note: See Annuity in Quicker BMLRS
Question 17.
Suppose your mom decides to gift you ₹ 10,000 every year starting from today for the next sixteen years. You deposit this amount in a bank as and when you receive and get 8.5% per annum interest rate compounded annually. What is the present value of this money: [Given that P (15, 0.085) = 8.304236] [1 Mark, Dec. 2015]
(a) 83,042
(b) 90,100
(c) 93,042
(d) 10,100
Answer:
(c) is correct
PV = 10,000[1−(1+8.5100)(−16−1)8.5 × 100 + 1]
= 10,000(8.304236 + 1)
= ₹ 93,042
Question 18.
The future value of an annuity of ₹ 1500 made annually for 5 years at an interest rate of 10% compounded annually is
[Given that (1.1 )5 = 1.61051] [1 Mark, 2017 June]
(a) 9517.56
(b) 9157.65
(c) 9715.56
(d) 9175.65
Answer:
FV = 1500[(1+10100)5−110 × 100]
Use Calculator tricks [See Quicker BMLRS]
= ₹ 9157.65
Question 19.
What sum should be invested at the end of every year so as to accumulate an amount of ₹ 796870 at the end of 10 years at the rate of interest 10% compounded annually, [given that A(10 ; 0.1) = 15.9374]
(a) 40,000
(b) 4,50,000
(c) 4,80,000
(d) 50,000
Answer:
Calculator Tricks: See[Quicker BMLRS] chap. Annuity 796870
R = 796870⎡⎣⎢(1+10100)10−110×100⎤⎦⎥
= ₹ 50,000
option (d) is correct.
Question 20.
A person invests ₹ 2,000 at the end of each month @ of interest 6% compounding monthly, find the amount of annuity after the 10th payment is :
Answer:
(a)
FV = 2000[(1+61200)10−16 × 1200]
= ₹ 20,456
Calculator Tricks : See calculator tricks in Quicker BMLRS
Type 6 ÷ 1200 +1 then press x button then = button 9 times -1 + 6 x 1200 x 2000 = button ; we will get the required result.
