Question

A person deposited Rs 60000 in a bank for 2 years at the rate of 10%pa compounded annually.But after one year,bank has changed the policy and decided to pay semi-annual compound interest at the same rate.What is the percentage difference between compound interest of first year and second year?

Answer 1

Answer:

$1.159\%$

Step-by-step explanation:

Given: Principal or P $=\textrm{Rs }60,000$.

Rate or R $=10\%$ per annum compounded annually.

Time or T $=2$ years.

To find: Percentage difference between compound interest of first year and second year.

Solution:

First year interest $=\frac{\textrm{P}\times \textrm{R}\times \textrm{T}}{100}=\frac{60000\times 10\times 1}{100}=\textrm{Rs }6000$.

First year amount $=\textrm{Rs }60,000+\textrm{Rs }6,000=\textrm{Rs }66,000$.

For the second year, the interest is compounded semi-annually.

So, time is doubled and the rate is halved.

Second year compounded amount $=66,000\times [1+\frac{10}{2\times 100}]^2=66,000\times1.1025=\textrm{Rs }72,765$.

Second year compound interest $=\textrm{Rs }72,765-\textrm{Rs }66,000=\textrm{Rs }6,765$.

Difference in interest of first and second year $=\textrm{Rs }6,765-\textrm{Rs }6,000=\textrm{Rs }765$.

Percentage difference $=\frac{765}{66000}\times 100\%=1.159\%$.

Hence, the percentage difference between compound interest of first year and second year is $1.159\%$.