Question

Mukesh borrowed Rs.75,000 from a bank. If the rate of interest is 12 % per annum, find the amount he would be paying after 1.5​ years if the interest is:
(1)compounded annually
(2)compounded half yearly

(a) (1) Rs. 88500, (2)Rs. 94080
(b) (1) Rs. 88897, (2)Rs. 89326
(c) (1) Rs. 94990 , (2)Rs. 74680
(d) (1) Rs. 74680 , (2)Rs. 94990

Answer 1

Hint: For the first part use the following formula: $A=P{(1+{\displaystyle \frac{R}{100}})}^T$ to calculate the amount.

Complete step-by-step answer:
In the second part use the following formula to calculate the final amount: $A=P{(1+{\displaystyle \frac{R}{200}})}^{2T}$.


In this question, we are given that Mukesh borrowed Rs.75,000 from a bank. The rate of interest is 12 % per annum.

We need to find the amount he would be paying after 1.5​ years if the interest is:

(1)compounded annually

(2)compounded half yearly

Let us first see the part (1) where interest is compounded annually.

If Mukesh borrowed Rs. 75,000 from a bank and the rate of interest is 12% per annum,

P = Rs. 75000

R = 12%

T = 1.5​ years

We know that for compound interest, the formula for the total amount when interest is compounded annually is given by the following:
$A=P{(1+{\displaystyle \frac{R}{100}})}^T$

Substituting the given values in this formula, we will get the following:

$A=75000{(1+{\displaystyle \frac{12}{100}})}^{{\displaystyle \frac{3}{2}}}$ = Rs. 88897.2

This is the answer for the first part.

Now, we will look into part (2).

We know that for compound interest, the formula for the total amount when interest is compounded half yearly is given by the following:

$A=P{(1+{\displaystyle \frac{R}{200}})}^{2T}$

Substituting the given values in this formula, we will get the following:

$A=75000{(1+{\displaystyle \frac{12}{200}})}^{2\times {\displaystyle \frac{3}{2}}}$ = Rs. 89326.2

This is the answer for part (2).

So, option (b) is correct.

Note: In this question, it is very important to know that for compound interest, the formula for the total amount when interest is compounded annually is given by the following: $A=P{(1+{\displaystyle \frac{R}{100}})}^T$. And that the formula for the total amount when interest is compounded half yearly is given by the following: $A=P{(1+{\displaystyle \frac{R}{200}})}^{2T}$ .