# Simple interest and compound interest

29 April 2020

##### Practice Questions For Simple Interest and Compound Interest

Q1) A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs.854 in 4 years. What is the sum?

A) Rs.650

B) Rs.700

C) Rs.698

D) Rs.690

Video Solution :

Q2) Arun took a loan of Rs.1400 with simple interest for as many years as the rate of interest. If he paid Rs.???????686 as interest at the end of the loan period, what was the rate of interest?

A) 6%

B) 8%

C) 7%

D)  4%

Video Solution :

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Q3) A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits 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:

A) Rs.121

B) Rs.120

C) Rs.123

D) Rs.122

Video Solution :

Q4) What is the difference between the compound interests on Rs.5000 for 1(1/2) years at 4% per annum compounded yearly and half-yearly?

A) Rs.2.04

B) Rs.3.06

C) Rs.8.30

D) Rs.4.80

Video Solution :

Q5) At what rate percent per annum will a sum of money double in 8 years.

A) 12.5%

B) 13.5%

C) 11.5%

D) 14.5%

Solution :

Let principal = P, Then, S.I.= P and Time = 8 years
We know that S.I. = PTR/100
Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum

Q6) A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

A) Rs. 650

B) Rs. 690

C) Rs. 698

D) Rs. 700

Solution :

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.

Q7) What is the rate of simple interest?
I. The total interest earned was Rs. 4000.
II. The sum was invested for 4 years.

A) Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

B) Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.

C) Statement I or in Statement II alone are sufficient to answer the question.

D) Statements I and II together are not sufficient to answer the question.

Solution :

We know that, R = (100* S.I)/(P*T).
Now, I gives, S.I. = Rs. 4000.
II gives, T = 4 years.
But, P is unknown. So, we cannot find R.
So, given data is insufficient to get R.

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Q8) Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually

A) 2109

B) 3109

C) 4109

D) 6109

Solution :

Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+(15/100))^2 X (1+((1/3)*15)/100)]
= Rs. [8000 * (23/20) * (23/20) * (21/20)]
= Rs. 11109. .
:. C.I. = Rs. (11109 - 8000) = Rs. 3109.

Q9) Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.

A) Rs. 610

B) Rs. 612

C) Rs. 614

D) Rs. 616

Solution :

Amount=[7500×(1+4/100)2]=(7500×26/25×26/25)=8112

Q10) The simple interest on a sum of money for 3 years at 6²/3 % per annum is \$ 6750. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?

A) 8125

B) 6655

C) 4496

D) 7210

Solution :

Given, SI = \$ 6750, R = 203% p.a. and T = 3 years.
sum = 100 × SI / R × T
= \$ (100 × 6750 × ³/20 × 1/3 ) = \$ 33750.
Now, P = \$ 33750, R = 203% p.a. and T = 3 years.
Therefore, amount after 3 years
= \$ {33750 × (1 + (20/3 × 100)}³ [using A = P (1 + R/100)]
= \$ (33750 × 16/15 × 16/15 × 16/15) = \$ 40960
Thus, amount = \$ 40960
Hence, compound interest = \$ (40960 - 33750) = \$ 7210

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