Compound Interest Quiz Set 014

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Question 1

An interest rate of 14% compounded half-annually is offered by a bank. An account holder deposits Rs. 60000 in the bank under this scheme. After six months he again deposits Rs 60000. What is the total amount that he will get after 1 year?

 A

Rs. 132894.

 B

Rs. 146476.

 C

Rs. 146276.

 D

Rs. 146576.

Soln.
Ans: a

Let P, A, r and n have their usual meanings. For the first deposit n = 2, and for the second deposit n = 1. So total amount is P × $((1 + r/100)^2 + (1 + r/100))$ = $P/10000$ × $((100 + r)^2 + 100(100 + r))$ = $P/10000 × (100 + r)$ × $(100 + r + 100)$ which equals ${P × (100 + r) × (200 + r)}/10000.$ Putting r = 7 and P = 60000 and cancelling 10000, we get 6 × 107 × 207 = Rs. 132894. Please note that the rate of interest will be 1/2 because the compounding is half yearly.


Question 2

An interest rate of 14% compounded half-annually is offered by a bank. An account holder deposits Rs. 30000 in the bank under this scheme. After six months he again deposits Rs 30000. What is the total amount that he will get after 1 year?

 A

Rs. 66447.

 B

Rs. 46476.

 C

Rs. 76276.

 D

Rs. 65577.

Soln.
Ans: a

Let P, A, r and n have their usual meanings. For the first deposit n = 2, and for the second deposit n = 1. So total amount is P × $((1 + r/100)^2 + (1 + r/100))$ = $P/10000$ × $((100 + r)^2 + 100(100 + r))$ = $P/10000 × (100 + r)$ × $(100 + r + 100)$ which equals ${P × (100 + r) × (200 + r)}/10000.$ Putting r = 7 and P = 30000 and cancelling 10000, we get 3 × 107 × 207 = Rs. 66447. Please note that the rate of interest will be 1/2 because the compounding is half yearly.


Question 3

The amount of Rs. 7000000 earns an interest of Rs. 1103375 @5% compounded annually. What is the investment period in years?

 A

3 years.

 B

2 years.

 C

1 year.

 D

1/2 year.

Soln.
Ans: a

The amount is 7000000 + 1103375. So 8103375 = 7000000 × $(105/100)^n$. So $8103375/7000000$ = $(105/100)^n$, which can be put in the form $(105/100)^3$ = $(105/100)^3$, so n = 3 years.


Question 4

The difference between compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 8. What is the rate p.a. if principal is Rs. 20000?

 A

2%.

 B

4%.

 C

3%.

 D

5%.

Soln.
Ans: a

If d is the difference, r is the rate and P is the principal, then the shortcut formula for the difference between compound and simple interest over a period of 2 years is d = P × $(r/100)^2$. So rate = 100 × $√{d/P}$ = 100 × $√{8/20000}$ = 2%.


Question 5

The interest earned by an amount of Rs. 90000 @2% compounded annually is Rs. 3636. What is the period in years?

 A

2 years.

 B

3 years.

 C

1 year.

 D

1/2 year.

Soln.
Ans: a

The amount is 90000 + 3636. So 93636 = 90000 × $(102/100)^n$. So $93636/90000$ = $(102/100)^n$, which can be put in the form $(102/100)^2$ = $(102/100)^n$, so n = 2 years.


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This Blog Post/Article "Compound Interest Quiz Set 014" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.

Posted by Parveen(Hoven),
Aptitude Trainer


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