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

`1.159\%`

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}* \textrm{R}* \textrm{T}}{100}=(60000* 10* 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* [1+(10)/(2* 100)]^2=66,000*1.1025=\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
`=(765)/(66000)* 100\%=1.159\%`.

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