Question

Find the compound interest of ₹ 96000 in `1 1/2` year at 5% per annum compounded half-yearly.

Answer 1

Step 1: Adjust the rate and time for half-yearly compounding.

The principal sum (P) is ₹ 96000, the annual interest rate (r) is 5% or 0.05 and the time (t) is `1 1/2` years.

Since the interest is compounded half-yearly, we need to adjust the rate and time for the compounding periods.

The rate per compounding period (r’) is half of the annual rate:

`r^’ = 0.05/2`

r’ = 0.025

The number of compounding periods (n) is the number of half-years in the given time:

`n = 1 1/2 xx 2`

n = 3 periods

Step 2: Calculate the final amount.

The formula for the amount (A) with compound interest is A = P(1 + r’)ⁿ.

A = 96000(1 + 0.025)³

A = 96000(1.025)³

A = 96000(1.076890625)

A = 103381.5

Step 3: Calculate the compound interest.

The compound interest (CI) is the difference between the final amount and the principal sum.

C.I. = A – P

C.I. = 103381.5 – 96000

C.I. = 7381.5

The compound interest is ₹ 7381.5.