Compound Interest Questions and Answers updated daily – Aptitude

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Compound Interest Questions

1. Aditya and Bhushan invested 10000 each in scheme A and scheme B respectively for 3 years. Scheme A offers Simple interest @ 12% per annum and scheme B offers compound interest @ 10%. After 3 years, who will have larger amount and by how much?      




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Correct Ans:Aditya, 290
Explanation:
Lets first calculate the total rate % that Aditya will have after 3 years:

As per the question Aditya invested at rate of 12% pa simple interst

So, for 3 years tenure he will get = 12 * 3 = 36%

And the amount that Bhushan invested at rate of 10% pa compound interest

By net% effect formula, we can calculate the total perecntage for 3 years tenure = 33.1% (sub details)

So, the difference between SI and CI = 36% – 33.1% = 2.9% (SI is more)

Here Aditya will get, 2.9% of 10000 = 290

So Aditya will have Rs. 290 more than Bhushan.

---------------------------------------------------------------------------------
Sub-details:-

Net% effect = x + y = xy/100 %

For the first 2 years: Here, x = y = 10%

= 10 + 10 = 10* 10 = 21 /100 %

And for the next year: Here x = 21% and y = 10%
= 21 + 10 = 21 * 10 = 33.1/100 %

Hence, option C is correct.
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2. A man gave 50% of his savings of Rs 67,280 to his wife and divided the remaining sum between his two sons A and B of 14 and 12 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was       




SHOW ANSWER
Correct Ans:Rs. 16000
Explanation:
Total Income = 67,280

After giving 50% salary to his wife the man is left with an amount = 33,640

Let's assume the man gave Rs. x to A. Therefore B will get Rs. (33640 – x).

↙ 33640 ↘
14 years A 12 years B
x (33640 – x)
Now, as per the question A & B will be getting an equal amount with CI at 5% rate per year at the 18th year.

⇒ x (1 + 5/100)4 = (33640 – x)[1+ 5/100] 6

---> x/(33640 – x) = (1 + 5/100 ) 6/(1 + 5/100) 4

⇒ x/(33640 – x) = = (21/20* 21/20)
⇒ 400 x = 33640 * 441 – 441x

⇒ 841x = 33640 *441

----> x = 33640 * 441/841 = 40 * 441 = 17640/-

Therefore, at the time of divison of money, B would have got a sum = (33640 – 17640) = Rs. 16000

Hence, option D is correct.
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3. Shantanu borrowed Rs. 2.5 lakh from a bank to purchase one car. If the rate of interest be 6% per annum compounded annually, what payment he will have to make after 2 years 6 months?




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Correct Ans:2,89,325
Explanation:
----> CI for 2 years 6 months at the rate of 6, applying the net% effect for first 2 years
----> = 6 + 6 + (6 * 6)/100 = 12.36%
----> Rate of interest for 6 months = (6/12) * 6 = 3%

----> For next 6 months = 12.36 + 3 + (12.36 * 3) /100 = 15.36 + 0.37% = 15.73%
----> Here, we can see that in 2 years 6 months the given compound rate of interest is approximate 15.73%.
----> Now, 115.73% of 250000 = (115.73 * 250000)/100 = 289,325.
----> Hence, option D is correct.
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4. Mr. Bede wins Rs. 120000 on Kaun Banega Crorepati. He has to pay 25% as gift tax to the government. He places remaining money in fixed deposit @ 10% compounded annually. However, he has to pay 20% tax on the interest. How much money does Mr. Bede has after 4 years?




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Correct Ans:Rs. 122444
Explanation:
Bede has Rs 90000 with him after paying 25% as gift tax.




So, Bede has Rs. (113374.08 + 11337.408 – 2267.4816) = Rs. 122444 at the end of 4th year.

Hence, option (A) is correct.
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5. A person closes his account in an investment scheme by withdrawing Rs 10000. One year ago, he had withdrawn Rs 6000. Two years ago he had withdrawn Rs 5000. Three years ago he had not withdrawn any money. How much money had he deposited approximately at the time of opening the account 4 years ago, if the annual rate of compound interest is 10%.




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Correct Ans:Rs. 15470
Explanation:
Suppose the person has deposited Rs. X at the time of opening account.
---> After one year, he had
----> Rs. (x + x * 10 * 1/100) = Rs. (11x/10)
----> After two years, he had
-----> Rs.((11x/10)+(11x/10) * (10 * 1/100)) = (121x/100)
----> After withdrawing Rs 5000 from Rs. (121x/100) ,the balance
----> = Rs. (121x - 500000/100)
---> After 3 years, he had
----> ((121x - 500000/100) + (121x - 500000/100) * (10 * 1/100))
----> = 11(121x - 500000/1000)
----> After withdrawing 6000 from above, the balance
----> = Rs.(1331x/1000) – 11500
----> After 4 years, he had
----> Rs.(11/10) ((1331x/1000) – 11500) - 10000 = 0
----> Rs 15470
Hence, option (A) is correct.
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6. Pankaj borrowed a total amount of Rs.32500 from his three friends Raj, Akash and Suresh. All of his friends apply different rates of interest in such a way that Raj applies 12%, Akash applies 16% and Suresh applies 18% interest rate respectively and total he gives Rs.5090 as interest. If the amount that Pankaj had taken from Raj is (18/25) of the amount taken from Suresh, then find that what amount Pankaj has taken from Akash?




SHOW ANSWER
Correct Ans:Rs. 11000
Explanation:
---> Let the amount taken from Suresh is x and amount taken from Raj = (18x/25)
---> Amount taken from Akash = 32500 – x – (18x/25) = 32500 – (43 x/25)
---> Total interest he gives :
---> ((18x/25) * 12/100) + (32500 – (43 x/25) * 16 /100) + ((x * 18)/100 ) = 5090 (Given)
---> 216x – 688x + 450x = 12725000 – 13000000
---> 22x = 275000
---> x = 12500
---> Amount taken from Akash
---> = 32500 – 43 * ( 12500 /25) = 32500 – 21500 = Rs.11000
---> Hence, option (C) is correct.
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7. The Ratio of Principal and three years C.I is 216 : 127. the difference between 3rd year C.I and 2nd year C.I is Rs.245. find out the difference between C.I and S.I of same sum of money for 2 years if rate of interest increased by 38%.




SHOW ANSWER
Correct Ans:399.9
Explanation:
Given: Principal = 216x; C.I = 127x
Amount = 216x + 127x = 343x
For three years ratio of amount and principal
A = P(1 + r/100)n
A/P = 343x/216x = (1 + r/100)3
1 + r/100 = ∛(343/216)
1 + r/100 = 7/6
r/100 = 7/6 - 1 = 1/6
r = 100/6 = 50/3 = 16(2/3)%

3rd year C.I - 2nd year C.I = 245
(3 years C.I - 2 years C.I) - (2 years C.I - 1st years C.I) = 245
3 years C.I - 2 * (2 years C.I) + 1st years C.I = 245
P[(1 + r/100)3 - 1] - 2*P[(1 + r/100)2 - 1] + P[(1 + r/100)1 - 1] = 245
P[(1 + r/100)3 - 1 - 2*(1 + r/100)2 + 2 + 1 + r/100 - 1] = 245
P[1 + 3r/100 + 3r2/1002 + r3/1003 + 1 - 2(1 + r2/1002 + 2r/100) + r/100] = 245
2 + 3r/100 + 3r2/1002 + r3/1003 - 2 - 2r2/1002 - 4r/100 + r/100 = 245
P(r2/1002 + r3/1003) = 245
Pr2/1003 * (100 + r) = 245
P*(50/3)2/1003 * (100 + (50/3)) = 245
P/(4*100*9) * (350/3)= 245
P/(8*9) * (7/3) = 245
P = (245*8*9*3)/7 = 7560

Increased rate of interest = 100/6 * 138/100 = 23%
The difference between C.I and S.I of same sum of money for 2 years = P[(1 + r/100)2 - 1] - Pnr/100
= P[1 + r2/1002 + 2r/100 - 1 - 2r/100]
= P(r2/1002)
= (7560*23*23) / (100*100) = Rs. 399.9
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8. Ratio of numerical value of rate of interest and time period is 4 : 1. Man invested Rs. 2400 and gets Rs. 864 as simple interest. Find the value of X, if man invested Rs. (2400 + X) at same rate of interest on C.I. for two years and get Rs. 814.08 as interest ?




SHOW ANSWER
Correct Ans:Rs. 800
Explanation:
Let man invested at the rate of 4x % per annum and for the period of time is x yr
ATQ
(2400 * 4x * x)/100 = 864
4x2 = 864/24
4x2 = 36
x2 = 9
x = 3
So, Rate of interest = 4 * 3 = 12% per annum
Time of period = 3 years.
Equivalent C.I. of two year at the rate of 12% per annum
CI = P[(1 + r/100)n - 1]
814.08 = (2400 + x) [(1 + 12/100)2 - 1]
814.08 = (2400 + x) [(112/100)(112/100) - 1]
814.08 = (2400 + x) [(28/25)(28/25) - 1]
814.08 = (2400 + x) [784/625 - 1]
814.08 = (2400 + x) [(784 - 625)/625]
814.08 = (2400 + x) (159/625)
814.08*(625/159) = 2400 + x
3200 = 2400 + x
x = 3200 - 2400 = 800
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9. A man invested (x - 1000) in scheme "˜A"™ which offer 30% p.a at CI and Rs. (x + 1000) in scheme "˜B"™ which offers 20% p.a. at SI. If he earns Rs. 5160 as interest after 2 years, then find the amount invested by him in scheme "˜B"™ ?




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Correct Ans:6000
Explanation:
Given, C.I + S.I = 5160
[(x - 1000)(1 + 30/100)2 - (x - 1000)] + [(x + 1000)*20*2]/100 = 5160
[(x - 1000) * 69/100] + [(x + 1000) * 40/100] = 5160
69x - 69000 + 40x + 40000 = 516000
109x = 516000 + 29000
x = 545000/109 = 5000
Amount invested on scheme B = 5000 + 1000 = Rs. 6000
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10. An amount was lent for one year at the rate of 18% per annum compounding annually. Had the compounding been done half yearly, the interest would have increased by Rs. 324. What was the amount (in Rs.) lent?




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Correct Ans:40000
Explanation:
Let the principal be 'x'.
Amount lent for 1 yr at 18% per annum compounding annually,
WKT, Amount = P (1 + r/100)n
Amount = x(1 + 18/100)
= 1.18x

When compounding been done half yearly,
r = 9%; n = 2 yr
Amount = x( 1 + 9/100)2
= 1.1881x
As per the question,
1.1881x - 1.18x = 324
0.0081x = 324
x = 324/0.0081
x = Rs. 40,000
Hence, the principal amount is Rs. 40,000.
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11. A tape recorder is sold for Rs. 3500 cash, or Rs. 1000 cash down payment and the balance in three equal easy installments. If 12(1/2)% is the rate of interest compounded annually, find the amount of installment.




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Correct Ans:Rs.1049.83
Explanation:
Let each installment be Rs. X.
Remaining amount = 3500 - 1000 = Rs. 2500
WKT, Amount = P[1+ (r/100)]n
Balance payment in three equal installments,
X/[1 + (25/200)] + X/[1 + (25/200)]2 + X/[1 + (25/200)]3 = 2500
[8/9]X + [8/9]2X+ [8/9]3X = 2500
(8/9)X*[1 + (8/9) + (64/81)] = 2500
(8/9)X*[(81 + 72 + 64)/81] = 2500
(8/9)X * (217/81) = 2500
X = (2500 * 9 * 81)/(8 * 217) = Rs 1049.83.
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12. Rs. 39,030 is divide between A and B in such a way that amount given to A on C.I. in 7 years is equal to amount given to B on C.I. in 9 years. Find the part of A. If the rate of interest is 4%.




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Correct Ans:Rs. 20,280
Explanation:
Given:
Let the principal of A and B be 'a' and 'b' respectively.
Amount = Rs. 39,030
r = 4%
Amount given to A for 7 yrs = Amount given to B for 9 yrs
WKT, Amount = P[1+ (r/100)]n
a[1 + (4/100)]7 = b[1 + (4/100)]9
a/b = [1 + (4/100)]9/[1 + (4/100)]7
a/b = [1 + (4/100)]2/1
a/b = [26/25]2/1
a : b = 676/625
a : b = 676 : 625
Part of A = 39030*(676/1301) = Rs. 20,280.
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13. Mukund and Bashid have equal amounts. Mukund invested all his amount at 10% p.a compounded annually for 2 years and Bashid invested 1/4th amount at 10% p.a compound interest (annually) and rest at r% per annum at simple interest for the same 2 years period. The amount received by both at the end of 2 year is same. What is the value of r?




SHOW ANSWER
Correct Ans:10.50%
Explanation:
Let amount of Mukund and Bashid each has = Rs. 400
Given, Mukund invested all his amount at 10% p.a compounded annually for 2 years
---> Compound Amount = P * [1 + (r/100)]n
= 400 * [1 + (10/100)]2
= 400 * [11/10]2
= 400 * [121/100]
= 484

Given, Bashid invested 1/4th amount (i.e, 400/4 = Rs. 100) at 10% p.a compound interest (annually)
---> Compound Amount = 100 * [1 + (10/100)]2
= 100 * [121/100]
= 121

Given, Bashid invested rest of the amount (ie., Rs. 300) at r% per annum at simple interest for the same 2 years period
---> Simple Interest = p*n*r /100
= (300 * 2 * r)/100
= 6r

Given, The amount received by both at the end of 2 year is same
---> 484 = 121 + 300 + 6r
---> 484 = 421 + 6r
---> 6r = 63
---> r = 10.5%
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14. Divide Rs. 3364 between Aakash and Bhaswan, so that Aakash's Share at the end of 5 years may equal to Bhaswan's share at the end of 7 years, compound interest being at 5 percent.




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Correct Ans:Rs. 1764 and Rs.1600
Explanation:
Given, Compound Interest, rate = 5%
W.K.T: Compound Amount = P [1 + (R/100)]n
Here, Principal amount (P) = Present share of Aakash/ Bhaswan

Given, Aakash's share after 5 years = Bhaswan's share after 7 years
----> (Aakash's present share) [1 + (5/100)]5 = (Bhaswan's present share) [1 + (5/100)]7
---> (Aakash's present share) / (Bhaswan's present share) = [1 + (5/100)]7/ [1 + (5/100)]5
---> (Aakash's present share) / (Bhaswan's present share) = [1 + (5/100)](7 - 5)
---> (Aakash's present share) / (Bhaswan's present share) = [1 + (5/100)]2
---> (Aakash's present share) / (Bhaswan's present share) = [1 + (1/20)]2
---> (Aakash's present share) / (Bhaswan's present share) = [21/20)]2
---> (Aakash's present share) / (Bhaswan's present share) = [441/400)]
i.e, Aakash's present share : Bhaswan's present share = 441 : 400

Since the total present amount is Rs. 3364,
Aakash's present share = [441/(441+400)] * 3364
= [441/(841)] * 3364
= Rs. 1764

Bhaswan's present share = Total present amount - Aakash's present share
= 3364 - 1764
= Rs. 1600
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15. Reyansh took loan from Canara Bank for his 2 years course of MBA at IMD. He took the loan of Rs. 6 lakh such that he would be charged at 8% per annum at CI during his course and at 10% CI after the completion of course. He returned half of the amount which he had to be paid on the completion of his studies and remaining after 2 years. What is the total amount returned by Reyansh?




SHOW ANSWER
Correct Ans:Rs. 7.733232 lakh
Explanation:
We know the formula for compound Amount:
Compound Amount = P [1 + (r/100)]n
Where,
P = Principal
r = Rate of interest
n = Time period

For the 2 years duration of his course,
Final amount to be paid after 2 years = 600000 * [1+ (8/100)]2
= 600000 * [108/100]2
= 60 * 108 * 108
= 6.99840 lakh

Of this amount, he paid half after completing his course.
So, he paid = (6.9984/2) = 3.4992 lakh
So, new remaining principal = 3.4992 lakh

After another 2 years at 10% rate,
Amount to be paid = 349920 * [1 + (10/100)]2
= 349920 * [110/100]2
= 349920 * [121/100]
= 4.234032 lakhs

He paid this amount in addition to earlier 3.4992 lakhs.
So, total amount he paid = 3.4992 + 4.234032
= 7.733232 lakhs
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16. A sum of money, deposited at some rate percent per annum of compound interest, doubles itself in 4 years. In how many years will it become 16 times of itself at the same rate? 




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Correct Ans:16
Explanation:
Let the principal be Rs.100
Amount doubles itself in 4 years = Rs.200
WKT, Amount = P [1 + (r/100 )n]
200 = 100[1 + (r/100)4]
2 = [1 + (r/100)4] .....(i)

If sum become 16 times in the time n years,
1600 = 100[1 + (r/100)n]
16 = [1 + (r/100)n]
24 = [1 + (r/100)n] ....(ii)

Using (i) in (ii),
[1 + (r/100)4]4 = [1 + (r/100)n]
[1 + (r/100)]16 = [1 + (r/100)n]
Hence, n = 16 yrs.
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17. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs 1200 for 2 years at 10% per annum. The sum placed on simple interest is? 




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Correct Ans:Rs. 525
Explanation:
Given:
CI: P - Rs. 1200; N - 2yrs; R - 10%
WKT, C.I. = P[(1+R/100)N] – P
CI = 1200[(1+ 10/100)2] – 1200
= 1200[(11/10)2 - 1]
= 1200[(121 - 100)/100]
= Rs. 252

As per the question, SI is half of the CI
SI = 252/2 = Rs. 126
WKT, SI = PNR/100
126 = (P x 3 x 8)/100
P = (126 x 100)/(3 x 8)
P = Rs. 525.
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18. What annual payment will discharge a debt of Rs. 50,440 due in 3 years at 5% per annum compounded annually? 




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Correct Ans:Rs. 18,522
Explanation:
Let each annual installment = Rs. X.
WKT,
X[(100/(100 + R)) + (100/(100 + R))2 + ...... + (100/(100 + R))T] = Debt amount
X[(100/(100 + 5)) + (100/(100 + 5))2 + (100/(100 + 5))3] = 50440
X[(100/105) + (100/105)2 + (100/105)3] = 50440
X*(20/21)[1 + (20/21) + (20/21)2] = 50440
X*(20/21)[1 + (20/21) + (400/441)] = 50440
X*(20/21)[1261/441] = 50440
X = (50440*21*441)/(20*1261)
X = Rs. 18,522.
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19. Two people A and B invested Rs. 10000 each at 8% simple interest for 6 years. After that A invested the amount for 2 years at the rate of 10% compounded annually while B invested amount for 2 years at 12% per annum simple interest. Find the difference between the interests earned by two person.




SHOW ANSWER
Correct Ans:Rs. 444
Explanation:
Given:
At SI: P = Rs. 10,000; R = 8%; N = 6 yrs
WKT, SI = PNR/100
SI = (10000 x 8 x 6)/100 = Rs. 4800
Amount = Principal + Interest = 10000 + 4800 = Rs. 14,800

A invested the amount in CI at 10% for 2 yrs.
WKT, CI = P[1 + (R/100)]N - P
CI = 14800[1 + (10/100)]2 - 14800
= 14800[(11/10)2 - 1]
= 14800[(121/100) - 1]
= 14800[(121 - 100)/100]
= 14800(21/100)
= Rs. 3108.

A invested the amount in SI at 12% for 2 yrs.
SI = (14800 x 12 x 2)/100 = Rs. 3552
Required difference = 3552 - 3108 = Rs. 444.
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20. Siva invested an amount into two parts in the ratio of 4 : 3 on compound interest for two years at the rates of 20% & 15% respectively. If he exchange rate of interests, then he will get Rs. 705 less interest than earlier interest, then find how much simple interest he will get, if he invest total amount at the rate of 17.5% for two years? 




SHOW ANSWER
Correct Ans:Rs. 14,700
Explanation:
Given:
Shiva invested an amount into two parts in the ratio = 4 : 3
Let the total amount invested by Shiva be Rs. 7X.

WKT, If the rate of compound interest for 2 years is then equivalent rate of interest will be
CI = r + r + [(r x r)/100]

Equivalent rate of interest for 2 yrs at 20% = 20 + 20 + [(20 x 20)/100]
= 20 + 20 + 4 = 44%
Equivalent rate of interest for 2 yrs at 15% = 15 + 15 + [(15 x 15)/100]
= 129/4 = 32.25%

As per the question,
Amount invested in earlier interest - amount invested in exchange of interest = Rs. 705
[(4X)*44% + (3X)*32.25%] - [(4X)*32.25% + (3X)*44% ] = 705
[4X*(44/100) + 3X*(32.25/100)] - [4X*(32.25/100) + 3X*(44/100)] = 705
[1.76X + 0.9675X] - [1.29X + 1.32X] = 705
2.7275X - 2.61X = 705
0.1175X = 705
X = Rs. 6000
So, total amount invested by Shiva = 7x = 7(6000) = Rs. 42,000

Therefore, SI for 2yrs at 17.5% = PNR/100 = 42000 x 2 x 17.5/100
= Rs. 14,700.
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