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Aptitude - Compound Interest
Compound Interest is an addition to the principal so that the added interest also earns interest. This is covered under Arithmetic ability. Questions under this section are ideal for the following examinations:
- CAT
- MAT
- SSC
- CPO Examination
- Bank PO, RBI Examination
- IIFT
- Hotel Management
Before answering the below given questions, just look at the formulae covered under Compound Interest topic. Here, we've considered the following:
P = Principal, R%/annum = Rate, t = Time
Annual Interest
Half-Yearly Interest
Quarterly Interest
When rates are different for different years. Here, the different rate are considered as R1%, R2%, R3%, R4 for 1st, 2nd, 3rd and 4th year respectively.
The present worth of Rs. z due t years is given by:
Amount = P [1 + R⁄100]t
Amount = P [1 + (R⁄2)⁄100]2t
Amount = P [1 + (R⁄4)⁄100]4t
Amount = P(1 + R1⁄100)(1 + R2⁄100)(1 + R3⁄100)
Present Worth = z⁄(1 + R⁄100)t
Q 1 - Find Compound Interest on Rs. 7500 at 4% per annum for 2 years.
Answer - C
Explanation
Amount =Rs [7500x(1+ 4⁄100)2] =Rs [7500 x ( 26⁄25 x 26⁄25 )2] = Rs. 8112
→C.I= Rs. (8112 -7500) = Rs. 612.
Q 2 - Find Compound Interest on Rs. 8000 at 15% per annum for 2 years 4 months compounded annually.
Answer - B
Explanation
Time =2 years 4 months =24⁄12 years = 21⁄3 years.
Amount =Rs [8000x(1+ 15⁄100)2 x (1+1⁄3 ⁄100x 15)] = Rs. (8000 x 23⁄20 x23⁄20 x21⁄20 )
→ Rs. 11109.
→C.I= Rs. (11109 -8000) = Rs. 3109.
Q 3 - Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compound half-yearly.
Answer - B
Explanation
Principal =Rs. 10000; Rate= 2% per half year; Time =2 years =4 half-years.
Amount =Rs. [10000x(1+ 2⁄100)4 = Rs.(10000 x 51⁄50 x 51⁄50 x 51⁄50 x 51⁄50)
→ Rs. 10824.32.
→C.I= Rs. (10824.32 -10000) = Rs. 824.32.
Q 4 - Find the compound interest on Rs. 16,000 at 20% per annum for 9 months, compounded quarterly.
Answer - C
Explanation
Principal = Rs. 16000; Time = 9 months = 3 quarters;
Rate =20% per annum = 5% per quarter.
→ Amount = Rs. [ 16000 x ( 16000 x ( 1 + 5⁄100 ) 3 ] =Rs. ( 16000 x 21⁄20 x 21⁄20 x 21⁄20) = Rs. 18522.
→ C.I = Rs. (18522 - 16000) = Rs. 2522.
Q 5 - If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate.
Answer - A
Explanation
Clearly, Rate = 5% p.a., Time = 3 years, S.I. =Rs. 1200.;
So, Principal =Rs. ( 100 x 1200⁄3 x 5 ) = Rs. 8000.
→ Amount = Rs. [ 8000 x ( 1 + 5⁄100 ) 3 ] =Rs. ( 8000 x 21⁄20 x 21⁄20 x 21⁄20) = Rs. 9261.
→ C.I = Rs. (9261 - 8000) = Rs. 1261.
Q 6 - In what time will Rs. 1000 become Rs. 1331 at 10 % per annum compounded annually ?
Answer - A
Explanation
Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10 % p.a
Let the time be n years. Then,
[1000( 1 + 10⁄100 )n] = 1331 or (11⁄10 )n = (1331⁄1000 ) = ( 11⁄10 )3
→ n= 3 years.
Q 7 - If Rs. 500 amounts to Rs. 583.20 in two years compounded annually, find the rate of interest per annum.
Answer - B
Explanation
Principal = Rs. 500; Amount = Rs. 583.20; Time = 2 years.
Let the rate be R% per annum. Then,
[500( 1 + R⁄100 )2] = 583.20 or ( 1 +R⁄100 )2 = 5832⁄5000 ) = 11664⁄10000 )
→ ( 1 + R⁄100 )2]= 108⁄100 )2 or 1 + R⁄100 = 108⁄100 or R =8.
→ So, rate = 8 % p.a.
Q 8 - If the compound interest on a certain sum at 16 2⁄3 % for 3 years is Rs. 1270, find the simple interest on the same sum at the same rate and for the same period.
Answer - D
Explanation
C.I. = [ X x(1 + 50⁄3 x 100)3 - X ] = (343x⁄216- x) = 127x⁄216.
→ 127x⁄216 = 1270 or x = 1270 x 216⁄127 = 2160.
Thus, the sum is Rs. 2160.
→ S.I. = Rs. ( 2160 x 50⁄3 x 3 x 1⁄100 )= Rs. 1080.
Q 9 - The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is Rs. 631. Find the sum.
Answer - D
Explanation
Let the sum be Rs. x. Then,
C.I. = x (1 + 10⁄100)2 - x = 21x⁄100, S.I = ( X x 10 x 2⁄100) = X⁄5
→ (C.I.) -( S.I) = (21x⁄100 - X⁄5) = X⁄100.
→ X⁄100 = 631 x = 63100.
→ Hence, the sum is Rs. 63,100.
Q 10 - The difference between the compound interest and simple interest accrued on an amount of Rs. 18,000 in 2 Years was Rs. 405. What was the rate of interest p.c.p.a ?
Answer - B
Explanation
Let the rate be R% p.a Then,
[ 18000(1+R⁄100)2- 18000]- (18000 x R x 2⁄100) = 405
→18000[(100+R)2⁄1000-1-2R⁄100]=405
→ 18000[100+R)2-10000-200R⁄10000]=405
9⁄5R2 R2=(405 x 5⁄9) = 255 R = 15.
→ Rate=15%.
Q 11 - Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 4% per annum.
Answer - A
Explanation
x(1+4⁄100)7=(1301-x)(1+4⁄1009 x⁄(1301 - x)= (1+4⁄1002=(26⁄25x26⁄25)
→ 625x = 676 (1301-x) 1301x = 676 X 1301 x 676.
So, the two parts are Rs. 676 and Rs(1301 - 676) i.e. Rs. 676 and Rs.
625
Q 12 - A certain sum amounts to Rs. 7350 in 2 years and to Rs. 8575 in 3 years. Find the sum and rate percent.
Answer - A
Explanation
S.I. on Rs. 7350 for 1 year = Rs. (8575 - 7350) = Rs. 1225.
→ Rate =(100 x 1225⁄7350 x 1)% = 16 2⁄3%
→Let the sum be Rs. x. Then,
x(1+50⁄3 x 1002= 7350 X x 7⁄6x7⁄6= 7350 X= (7350 x 36⁄49)=5400.
→ Sum = Rs. 5400.
Q 13 - A sum of money amount to Rs. 6690 after 3 years and to Rs. 10,035 after 6 years on compound interest. Find the sum.
Answer - A
Explanation
P(1+ R⁄100)3 = 6690 ...(i) and P(1+ R⁄100)6 = 10035 ...(ii)
On Dividing, we get (1+ R⁄100)3= 10035⁄6690=3⁄2
Substituting this value in (i), we get:
P x 3⁄2=6690 or P = (6690 x 2⁄3) = 4460.
Hence, the sum is Rs. 4460.
Q 14 - A sum of money doubles itself at compound interest in 15 years. In how many years will it become eight times?
Answer - A
Explanation
P(1+ R⁄100)15 = 2P → (1+ R⁄100)15 = 2P⁄P =2 (i)
Lets P(1+R⁄100)n=8P → (1+ R⁄100)n=8 =23={(1+R⁄100)15}3 [using (i)]
→ (1+R⁄100)n = (1+ R⁄100)45 → n= 45.
Thus, the required time = 45 years.
Q 15 - What annual payment will discharge a debt of Rs. 7620 due in 3 years at 162⁄3% per annum compound interest?
Answer - B
Explanation
Lets each instalment be Rs. x. Then,
(P.W. of Rs x due 1 year hence) +(P.W. of Rs. x due 2 years hence) +(P.W. of Rs. x due 3 years hence)= 7620
→ X⁄(1+50⁄3 x 100)+X⁄(1+50⁄3 x 100)2+X⁄(1+50⁄3 x 100)3=7620
→ 6x⁄7+36x⁄49216x⁄343=7620 294x +252x +216x =7620 x 343
→ x=(7620 x 343⁄762) Rs. 3430.
.: Amount of each instalment =rs. 3430.
Q 16 - Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will albert get on maturity of the fixed deposit ?
Answer - D
→ Amount = Rs. [8000 x (1+ 5⁄100)2] =Rs. (8000 x 21⁄20 x 21⁄20) = Rs. 8820.
Q 17 - What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a. ?
Answer - C
→ Amount = Rs. [25000 x (1+ 12⁄100)3] =Rs. (25000 x 28⁄25 x 28⁄25 x 28⁄25) = Rs. 35123.20→ C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20
Q 18 - A man save Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
Answer - C
Amount = Rs. [200(1 + 5⁄100)3 +200 (1+5⁄100)2+200 (1+5⁄100)]→ Rs= [200 x 21⁄20x21⁄20x21⁄20+200 x 21⁄20x21⁄20+200x21⁄20]
→=Rs.[200x21⁄20(21⁄20 x 21⁄20 x 21⁄20 + 1)]= Rs. 662.02
Q 19 - Sam invested Rs. 15,000 @ 10% per annum for one year. if the interest is compounded half-yearly, then the amount received by sam at the end of the year will be :
Answer - C
+ = Rs. 15000; R = 10% p.a. = 5% per half year ; T = 1 year = 2 half years.→ Amount = Rs. [15000 x 15⁄100)2] = Rs. (15000 x 21⁄20 x 21⁄20 )
→ 16537.50
Q 20 - A bank offers 5% compound interest calculated on half-yearly basis. A customer deposited Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
Answer - B
Amount = Rs. [1600 x (1+ 5⁄2 x 100)2+1600 x (1 + 5⁄2 x 100)] → = Rs. [1600 x 41⁄40 x 41⁄40 +1600 x 41⁄40] → = Rs. [1600 x 41⁄40(41⁄40+1)] = Rs. (1600 x41 x81⁄40 x40 = Rs. 3321. → C.I. = Rs. ( 3321 - 3200) = Rs. 121.
Q 21 - What is the difference between the compound interests on Rs. 5000 for 11⁄2 years at 4% per annum compounded yearly and half-yearly ?
Answer - A
C.I. when interest is compounded yearly= Rs. [ 5000 x (1 + 4⁄100) x ( 1+ 1⁄2x 4⁄100)] = Rs. (5000 x 26⁄25 x 51⁄50) = Rs. 5304
C. I when interest is compounded half yearly = Rs. [ 5000 x ( 1 2⁄100)3] = Rs. (5000 x 51⁄50 x 51⁄50 x 51⁄50)= Rs. 5306.04
→ Difference = Rs. (5306.04 - 5304) = Rs. 2.04.
Q 22 - Find the compound interest on Rs. 15,625 for 9 months at 16% per annum compounded quarterly.
Answer - C
P = Rs. 15625, n =9 months = 3 quarters, R= 16% p.a. =4% per quarter.→ Amount = Rs. [ 15625 x ( 1+ 4⁄100)3] = Rs. (15625 x 26⁄25 x 26⁄25 x 26⁄25)= Rs.17576. → C.I. = Rs. (17576- 15625) = Rs. 1951.
Q 23 - If the simple interest sum of money for 2 years at 5% per annum is Rs. 50, what is the compound Interest on the same sum at the same rate and for the sum time?
Answer - A
Sum = Rs. (50 x 100⁄2 x 5) = Rs. 500.→ Amount = Rs. [500 x (1+5⁄1002 = Rs. ( 500 x 21⁄20 x 21⁄20) = Rs. 551.25.
→ C.I = Rs.(551.25 - 500) = Rs. 51.25.
Q 24 - What will be the difference between simple and compound interest @ 10% per annum on a sum of Rs. 1000 after 4 years?
Answer - D
S.I. = Rs. (1000 x 10 x 4⁄100) = Rs. 400.C.I. = Rs. [1000 x (1+10⁄100)2 - 1000] = Rs.464.10.
→ Difference = Rs. (464.10 - 400)= Rs. 64.10.
Q 25 - The difference between simple interest and compound interest on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
Answer - D
S.I. = Rs. (1200 x 10 x 1)⁄100) = Rs. 120.C.I. = Rs. [1200 x (5⁄100)2 - 1200] = Rs. 123.
→ Difference = Rs. (123 - 120) = Rs. 3
Q 26 - The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:
Answer - A
Amount = Rs. (30000 + 4347) = Rs. 34347Let the time be n years. Then, 30000(1+ 7⁄100n = 34347 (107⁄100)n = 34347⁄30000= 11449⁄10000= (107⁄100)2
→ n = 2 years.
Q 27 - At what rate of compound interest per annum will a sum of Rs. 1200 becomes Rs. 1348.32 in 2 years?
Answer - A
Let the rate be R% p.a. Then,1200 x (1 + R⁄100)2= 1348.32 (1 + R⁄100)2 = 134832⁄120000 = 11236⁄10000
→ (1 + R⁄100)2 = (106⁄100)2 or 1 + R⁄100=106⁄100 or R = 6%.
Q 28 - The principal that amounts to Rs. 4913 in 3 years at 61⁄4% per annum compound interest compounded annually, is:
Answer - D
Principal = Rs. [4913⁄(1+25⁄4 x 100)3] = Rs. (4913 x 16⁄17x 16⁄17x 16⁄17) = Rs. 4096.
Q 29 - In how many years will a sum of Rs. 800 at 10% per annum compounded semi-annually become Rs. 926.10?
Answer - B
Let the time be n years. Then,800x(1+5⁄100)2n = 929.10 or (1+5⁄100)2n = 9261⁄8000
→ or (21⁄20)2n = (21⁄20)3 or 2n = 3 or n= 3⁄2.
→ n=11⁄2 years.
Q 30 - If the compound interest on a sum for 2 years at 121⁄2% per annum is rs. 510, the simple interest on the same sum at the same rate for the same period of time is:
Answer - B
Let the sum be Rs. P.Then,[P(1+25⁄2 x 100) 2 - P] = 510 or p[(9⁄82 - 1] = 510 or P = (510 x 64 ⁄17) = 1920. → Sum Rs. 1920.
→ So, S.I. = Rs. (1920 x 25 x 2⁄2 x 100) = Rs. 480.
Q 31 - The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for bouble the time at half the rate percent per annum is:
Answer - B
Let the sum Rs. P. Then,P(1+10⁄100) 2 - P] = 525 p[(11⁄102 - 1] = 525 P = (525 x 100 ⁄21) = 2500.
→ Sum = Rs. 2500.
→ So, S.I = Rs. (2500 x 5 x 4⁄100) = Rs. 500.
Q 32 - The simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. the sum placed on simple interest is:
Answer - C
C.I = Rs. [4000 x (1+ 10⁄100)2-4000] = Rs. ( 4000 x 11⁄10 x 11⁄10- 4000) = Rs. 840.→ Sum = RS. (420 x 100⁄3 x 8) = Rs. 1750.
Q 33 - There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
Answer - C
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.→ R= 100 x 60⁄100 x 6 = 10% p.a.
Now, P = Rs. [12000, T = 3 years and R = 10% p.a.
&rarr C.I. = Rs [12000 x {(1+10⁄100)3 - 1}]= Rs. (12000 x 331⁄1000) = Rs. 3972.
Q 34 - The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs.96. What is the rate of interest per annum?
Answer - C
[15000 x (1+ R⁄100)2 -15000] - (15000 x R x 2⁄100) = 9615000 [ (1+R⁄100)2-1-2R⁄100= 96 15000[(100+R)2-10000-200R⁄10000]=96
R2= 96 x 2⁄3= 64 R= 8
→ Rate = 8%.
Q 35 - The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the period is Rs. 800. The difference between the compound interest and the simple interest for 3 years will be:
Answer - C
Difference in C.I. and S.I. for 2 years = Rs. 32.S.I. for one year = Rs. 400.
S.I. on Rs. 400 for one year = Rs. 32.
So, Rate = (100 x 32⁄400 x 1% = 8%.
Hence, difference in C.I. and S.I. for 3rd year
→ S.I. on Rs. 832. = Rs. (832 x 8 x 1⁄100) = Rs. 66.56
Q 36 - The difference between simple interest on a certain sum at the rate of 10% per annum for 2 years and compound interest which is compounded every 6 months is Rs. 124.05 What is the principal sum?
Answer - D
Let the sum be Rs. P. ThenP[(1+5⁄100)4-1] - P x 10 x 2⁄100 = 124.05
→ P[(21⁄20)4-1-1⁄5= 124.05 → P[194481⁄160000-6⁄5 = 12405⁄100
→ P[194481 - 192000⁄160000] = 12405⁄100 → P = (12405⁄100 x 160000⁄2481) = 8000.
Q 37 - The difference between compound interest and simple interest on a sum for 2 years at 10% per annum, when the interest is compounded anually is Rs. 16. If the interest were compounded half-yearly, the difference in two interest would be:
Answer - A
For first year, S.I =C.I.Now, Rs. 16 is the S.I. on S.I. for 1 year.
Rs. 10 is S.I. on Rs. 100.
→ Rs. 16 is S.I. on Rs. 100⁄10 x 16) = Rs. 160.
So, S.I. on Principal for 1 year at 10% is Rs. 160.
Principal = Rs. (100 x 160⁄10 x 1) = Rs. 1600.
Amount for 2 years compounded half yearly = Rs. [1600 x (1 + 5⁄100)4] = Rs. 1944.81
→ C.I. = Rs. (344.81 - 320) = Rs. 24.81.
→ (C.I.) - (S.I.)= Rs. (344.81- 320) = Rs. 24.81
Q 38 - A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs. 482 more, if the interest was payable helf-yearly then if it was payable annually
The sum is:
Answer - A
Let the sum be Rs. z. Then,C.I. when compounded half-yearly = [z x (1 + 10⁄100)4 - z ] = 4641⁄10000z.
→ C.I. when compounded annually = [z x(1+ 20⁄1002 - z ] = 11⁄25z.
→ 4641⁄10000z-11⁄25z = 482 or z = 482 x 10000⁄241 = Rs. 20000
Q 39 - On a sum of money, the simple interest for 2 years at Rs. 600, while the compound interest is Rs. 696.30, the rate of interest being the same in both the case. The rate of interest is:
Answer - A
Difference in C.I. and S.I. for 2 years = Rs.(696.30 - 660) = Rs. 36.30→S.I. for one year = Rs. 330.
→Rate (100 x 36.30⁄330 x 1)% = 11%.
Q 40 - The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
Answer - D
Amount of Rs. 100 for 1 year when compounded half-yearly→= Rs.[100 x(1+ 3⁄100)2] = Rs. 106.09.
→ Effective rate = (106.09 - 100% = 6.09.
Q 41 - Raman lent out a certain sum of simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25: 8.
The rate of interest per annum is:
Answer - D
Let the principal be Rs. P and rate of interest be R% per annum.Difference of C.I. and S.I. for 2 years.
= P[P x (1+R⁄100)2-P]-(P x R x 2⁄100)= PR2⁄104(300 + R⁄100).
→PR2⁄104300 + R⁄100⁄PR2⁄104= 25⁄8 => (300+R⁄100)= 25⁄8 => R= 100⁄8 = 121⁄2%.
Q 42. - Rahul invested money in two schemes A and B offering compound interest @ 8 p.c.p.a. and 9 p.c.p.a. respectively. If the total amount of interest accrued through two schemes together in two years was Rs. 4818.30 and the total amount invested was Rs. 27,000,
What was the amount invested in Scheme A ?
Answer - A
Let the investment by Rahul in scheme A be Rs. xThen, investment in scheme B= Rs. (27000 - x).
→ [x x {(1+8⁄100)2)-1}+(27000-x){(1+9⁄100)2- 1 }]=4818.30
→ (x x 104⁄625)+ 1881(27000-x)⁄10000= 481830⁄100
→ 1664x+1881(27000-x)= 48183000
→ 217x= 2604000 x= 2604000⁄217 = Rs. 12000
Q 43 - A sum of money invested at compound interest amounts to Rs. 800 in 3 years and to Rs. 840 in 4 years. The rate of interest per annum is:
Answer - C
S.I. on Rs. 800 for 1 year = Rs. (840-800) = Rs.40→ Rate= (100 x 40⁄800 x 1)% = 5%
Q 44 - A sum of money invested at compound interest amounts to Rs. 4624 in 2 years and to Rs. 4913 in 3 years. The sum of money is:
Answer - A
S.I. on Rs. 4624 for 1 year = Rs. (4913 - 4624) = Rs. 289.→ Rate = (100 x 289⁄4624 x 1) % = 61⁄4%.
→ Now, x(1 + 25⁄4 x 100)2 = 4624 or X x17⁄16 x 17⁄16 = 4624
→ x = (4624 x 16⁄17 x 16⁄17) = Rs. 4096.
Q 45 - A sum of Rs. 12,000 deposited at compopund interest become double after 5 years.
After 20 years, it will become:
The sum is
Answer - D
12000 x(1R⁄100)5 = 24000 => (1+R⁄100)5) = 2→ [(1+R⁄100)5]4 = 24 =16 => (1+ R⁄100)20 = 16 => P(1+ R⁄100)20 = 16P
=> 12000 (1+R⁄100)20 =16 x 12000 = Rs. 192000.
Q 46 - A sum of money placed at compound interest double itself in 5 years. It will amount to eight times itself at the same rate of interest in?
Answer - D
P(1+R⁄100)5 = 2P => (1+R⁄100)5 = 2Let P(1+R⁄100)n = 8P => (1+R⁄100n =8= 23={(1+R⁄100)5}3
=> (1+R⁄100)5 =(1+R⁄100)15 => n=15.
→ Required time = 15 years.
Q 47 - The least number of complete year in which a sum of money put out at 20% compound interest will be more then double is ?
Answer - B
P(1+20⁄100)n > 2P or (6⁄5)n > 2Now, (6⁄5 x 6⁄5 x 6⁄5 x6⁄5 ) > 2. So, n = 4 years.
Q 48 - A man borrows Rs. 2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be ?
Answer - B
Let the value of each instalment be Rs. x, Then, (P.W. of Rs. x due 1 year hence) + (P.W. of Rs. x due 2 years hence) = Rs. 2550→ x⁄(1+4⁄100 + x⁄(1+ 4⁄1002 =2550 25x⁄26 + 625x⁄676= 2550
→ 1275x = 2550x 676 x = (2250 x 676⁄1275) = 1352. → Value of each instalment = Rs. 1352
Q 49 - What annual payment will discharge a discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest?
Answer - B
Let each instalment be Rs. x. Then,→ x⁄(1+5⁄100 + x⁄(1+ 5⁄1002 =1025 25x⁄21 + 400x⁄441= 1025
820x = 1025 x 441 x = ( 1025 x 441⁄820) = 551.25.
So, value of each instalment = Rs. 551.25
Q 50 - A sum of money is borrowed and paid back in two annual instalments of Rs. 882 each allowing 5% compound interest. The sum borrowed was?
Answer - B
Principal=(P.W of Rs. 882 due 1 year hence) + (P.W. of Rs. 882 due 2 years hence)
=[882⁄(1+ 5⁄100) + 882⁄(1+ 5⁄100)2]= ( 882 x 20⁄21 + 882 x 400 ⁄441)
→ Rs. 1640.
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