# Compound Interest Questions and Answers updated daily – Aptitude

Compound Interest Questions: Solved 161 Compound Interest Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

## 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?

SHOW ANSWER

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 %

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.**
Workspace

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).

â†™ 33640 â†˜

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)

---> x/(33640 – x) = (1 + 5/100 )

⇒ 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

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).

â†™ 33640 â†˜

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.**
Workspace

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?

SHOW ANSWER

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.

---->

----> = 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.**
Workspace

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?

SHOW ANSWER

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 â€“ 2267.4816) = Rs. 122444 at the end of 4th year.

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

**Hence, option (A) is correct.**
Workspace

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%.

SHOW ANSWER

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) â€“ 11500

----> After 4 years, he had

----> Rs.(11/10) ((1331x/1000) â€“ 11500) - 10000 = 0

----> Rs 15470

---> 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) â€“ 11500

----> After 4 years, he had

----> Rs.(11/10) ((1331x/1000) â€“ 11500) - 10000 = 0

----> Rs 15470

**Hence, option (A) is correct.**
Workspace

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 â€“ x â€“ (18x/25) = 32500 â€“ (43 x/25)

---> Total interest he gives :

---> ((18x/25) * 12/100) + (32500 â€“ (43 x/25) * 16 /100) + ((x * 18)/100 ) = 5090 (Given)

---> 216x â€“ 688x + 450x = 12725000 â€“ 13000000

---> 22x = 275000

---> x = 12500

---> Amount taken from Akash

---> = 32500 â€“ 43 * ( 12500 /25) = 32500 â€“ 21500 = Rs.11000

--->

---> Amount taken from Akash = 32500 â€“ x â€“ (18x/25) = 32500 â€“ (43 x/25)

---> Total interest he gives :

---> ((18x/25) * 12/100) + (32500 â€“ (43 x/25) * 16 /100) + ((x * 18)/100 ) = 5090 (Given)

---> 216x â€“ 688x + 450x = 12725000 â€“ 13000000

---> 22x = 275000

---> x = 12500

---> Amount taken from Akash

---> = 32500 â€“ 43 * ( 12500 /25) = 32500 â€“ 21500 = Rs.11000

--->

**Hence, option (C) is correct.**
Workspace

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)

A/P = 343x/216x = (1 + r/100)

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)

P[(1 + r/100)

P[1 + 3r/100 + 3r

2 + 3r/100 + 3r

P(r

Pr

P*(50/3)

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)

= P[1 + r

= P(r

= (7560*23*23) / (100*100) = Rs. 399.9

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] = 245P[(1 + r/100)

^{3}- 1 - 2*(1 + r/100)^{2}+ 2 + 1 + r/100 - 1] = 245P[1 + 3r/100 + 3r

^{2}/100^{2}+ r^{3}/100^{3}+ 1 - 2(1 + r^{2}/100^{2}+ 2r/100) + r/100] = 2452 + 3r/100 + 3r

^{2}/100^{2}+ r^{3}/100^{3}- 2 - 2r^{2}/100^{2}- 4r/100 + r/100 = 245P(r

^{2}/100^{2}+ r^{3}/100^{3}) = 245Pr

^{2}/100^{3}* (100 + r) = 245P*(50/3)

^{2}/100^{3}* (100 + (50/3)) = 245P/(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 + r

^{2}/100^{2}+ 2r/100 - 1 - 2r/100]= P(r

^{2}/100^{2})= (7560*23*23) / (100*100) = Rs. 399.9

Workspace

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

4x

4x

x

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)

814.08 = (2400 + x) [(1 + 12/100)

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

ATQ

(2400 * 4x * x)/100 = 864

4x

^{2}= 864/244x

^{2}= 36x

^{2}= 9x = 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

Workspace

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"™ ?

SHOW ANSWER

Correct Ans:6000

Explanation:

Given, C.I + S.I = 5160

[(x - 1000)(1 + 30/100)

[(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

[(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

Workspace

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?

SHOW ANSWER

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)

Amount = x(1 + 18/100)

= 1.18x

When compounding been done half yearly,

r = 9%; n = 2 yr

Amount = x( 1 + 9/100)

= 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.

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.

Workspace

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.

SHOW ANSWER

Correct Ans:Rs.1049.83

Explanation:

Let each installment be Rs. X.

Remaining amount = 3500 - 1000 = Rs. 2500

WKT, Amount = P[1+ (r/100)]

Balance payment in three equal installments,

X/[1 + (25/200)] + X/[1 + (25/200)]

[8/9]X + [8/9]

(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.

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]

^{2}X+ [8/9]^{3}X = 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.

Workspace

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%.

SHOW ANSWER

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)]

a[1 + (4/100)]

a/b = [1 + (4/100)]

a/b = [1 + (4/100)]

a/b = [26/25]

a : b = 676/625

a : b = 676 : 625

Part of A = 39030*(676/1301) = Rs. 20,280.

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}/1a/b = [26/25]

^{2}/1a : b = 676/625

a : b = 676 : 625

Part of A = 39030*(676/1301) = Rs. 20,280.

Workspace

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

--->

= 400 * [1 + (10/100)]

= 400 * [11/10]

= 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)]

= 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

--->

= (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

--->

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%**
Workspace

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.

SHOW ANSWER

Correct Ans:Rs. 1764 and Rs.1600

Explanation:

Given, Compound Interest, rate = 5%

W.K.T: Compound Amount = P [1 + (R/100)]

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)]

---> (Aakash's present share) / (Bhaswan's present share) = [1 + (5/100)]

---> (Aakash's present share) / (Bhaswan's present share) = [1 + (5/100)]

---> (Aakash's present share) / (Bhaswan's present share) = [1 + (5/100)]

---> (Aakash's present share) / (Bhaswan's present share) = [1 + (1/20)]

---> (Aakash's present share) / (Bhaswan's present share) = [21/20)]

---> (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,

= [441/(841)] * 3364

=

= 3364 - 1764

=

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**
Workspace

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:

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)]

= 600000 * [108/100]

= 60 * 108 * 108

= 6.99840 lakh

Of this amount, he paid half after completing his course.

So,

So, new remaining principal = 3.4992 lakh

After another 2 years at 10% rate,

= 349920 * [110/100]

= 349920 * [121/100]

=

He paid this amount in addition to earlier 3.4992 lakhs.

So,

=

**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**
Workspace

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?

SHOW ANSWER

Correct Ans:16

Explanation:

Let the principal be Rs.100

Amount doubles itself in 4 years = Rs.200

WKT,

200 = 100[1 + (r/100)

2 = [1 + (r/100)

If sum become 16 times in the time n years,

1600 = 100[1 + (r/100)

16 = [1 + (r/100)

2

Using (i) in (ii),

[1 + (r/100)

[1 + (r/100)]

Hence, n = 16 yrs.

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}]2

^{4}= [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.

Workspace

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?

SHOW ANSWER

Correct Ans:Rs. 525

Explanation:

Given:

CI: P - Rs. 1200; N - 2yrs; R - 10%

WKT,

CI = 1200[(1+ 10/100)

= 1200[(11/10)

= 1200[(121 - 100)/100]

= Rs. 252

As per the question, SI is half of the CI

SI = 252/2 = Rs. 126

WKT,

126 = (P x 3 x 8)/100

P = (126 x 100)/(3 x 8)

P = Rs. 525.

CI: P - Rs. 1200; N - 2yrs; R - 10%

WKT,

**C.I. = P[(1+R/100)**^{N}] – PCI = 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.

Workspace

18. What annual payment will discharge a debt of Rs. 50,440 due in 3 years at 5% per annum compounded annually?

SHOW ANSWER

Correct Ans:Rs. 18,522

Explanation:

Let each annual installment = Rs. X.

WKT,

X[(100/(100 + 5)) + (100/(100 + 5))

X[(100/105) + (100/105)

X*(20/21)[1 + (20/21) + (20/21)

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.

WKT,

**X[(100/(100 + R)) + (100/(100 + R))**^{2}+ ...... + (100/(100 + R))^{T}] = Debt amountX[(100/(100 + 5)) + (100/(100 + 5))

^{2}+ (100/(100 + 5))^{3}] = 50440X[(100/105) + (100/105)

^{2}+ (100/105)^{3}] = 50440X*(20/21)[1 + (20/21) + (20/21)

^{2}] = 50440X*(20/21)[1 + (20/21) + (400/441)] = 50440

X*(20/21)[1261/441] = 50440

X = (50440*21*441)/(20*1261)

X = Rs. 18,522.

Workspace

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 = (10000 x 8 x 6)/100 = Rs. 4800

A invested the amount in CI at 10% for 2 yrs.

WKT,

CI = 14800[1 + (10/100)]

= 14800[(11/10)

= 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.

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. 14,800A invested the amount in CI at 10% for 2 yrs.

WKT,

**CI = P[1 + (R/100)]**^{N}- PCI = 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.

Workspace

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

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,

[(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.

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.

Workspace

Are you seeking for good platform for practicing Compound Interest questions in online. This is the right place. The time you spent in Fresherslive will be the most beneficial one for you.

## Online Test on Compound Interest @ Fresherslive

This page provides important questions on Compound Interest along with correct answers and clear explanation, which will be very useful for various Interviews, Competitive examinations and Entrance tests. Here, Most of the Compound Interest questions are framed with Latest concepts, so that you may get updated through these Compound Interest Online tests. Compound Interest Online Test questions are granted from basic level to complex level.

## Why To Practice Compound Interest Test questions Online @ Fresherslive?

Compound Interest questions are delivered with accurate answer. For solving each and every question, very lucid explanations are provided with diagrams wherever necessary.

Practice in advance of similar questions on Compound Interest may improve your performance in the real Exams and Interview.

Time Management for answering the Compound Interest questions quickly is foremost important for success in Competitive Exams and Placement Interviews.

Through Fresherslive Compound Interest questions and answers, you can acquire all the essential idea to solve any difficult questions on Compound Interest in short time and also in short cut method.

Winners are those who can use the simplest method for solving a question. So that they have enough time for solving all the questions in examination, correctly without any tense. Fresherslive provides most simplest methods to answer any tough questions. Practise through Fresherslive test series to ensure success in all competitive exams, entrance exams and placement tests.

## Why Fresherslive For Compound Interest Online Test Preparation?

Most of the job seekers finding it hard to clear Compound Interest test or get stuck on any particular question, our Compound Interest test sections will help you to success in Exams as well as Interviews. To acquire clear understanding of Compound Interest, exercise these advanced Compound Interest questions with answers.

You're Welcome to use the Fresherslive Online Test at any time you want. Start your beginning, of anything you want by using our sample Compound Interest Online Test and create yourself a successful one. Fresherslive provides you a new opportunity to improve yourself. Take it and make use of it to the fullest. GOODLUCK for Your Bright Future.