Question

12. The difference between the compound interest for 1 year, compounded half-yearly and the

simple interest for 1 year on a certain sum of money at 10% per annum is Rs. 360. Find the sum​

Answer 1

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Answer 2

Given :

The difference between the compound interest for 1 year, compounded half-yearly and the  simple interest for 1 year on a certain sum of money at 10% per annum is Rs. 360.

To Find:

Find the sum​

Solution:

Let the sum be x

Rate of interest = 10% = 0.1

Time = 1 year

No. of compounds per year = n = 2

$Amount = P(1+\frac{r}{n})^{nt}\\Amount = x(1+\frac{0.1}{2})^{2 \times 1}\\Amount = 1.1025x$

Compound Interest = Amount - Principal = 1.1025 x-x=0.1025x

Simple interest = $\frac{P \times T \times R}{100} =\frac{x \times 1 \times 10}{100}=0.1x$

The difference between compound interest and simple interest is Rs.360

So,0.1025x-0.1x=360

0.0025x=360

$x=\frac{360}{0.0025}$

x=144000

Hence the sum is Rs.144000