Learn How to Calculate Compound Interest when Interest is Compounded Half-Yearly. Computation of Compound Interest by the growing principal can be complicated. Check out Solved Examples explaining the step by step process for finding the compound interest when compounded half-yearly. To help you better understand we have given the Compound Interest Formula when Interest Rate is Compounded Half-Yearly.

## How to find Compound Interest when Interest is Compounded Half-Yearly?

If the rate of interest is annual and interest is compounded half-yearly then the annual interest rate is halved(r/2) and the number of years is doubled i.e. 2n. The Formula to Calculate the Compound Interest when Interest Rate is Compounded Half Yearly is given by

Let Principal = P, Rate of Interest = r/2 %, time = 2n, Amount = A, Compound Interest = CI then

A = P(1+r/2/100)^{2n}

In the Case of the Half-Yearly Compounding, Rate Interest is divided by 2 and the number of years is multiplied by 2.

CI = A – P

= P(1+r/2/100)^{2n} – P

=P{(1+r/2/100)^{2n}-1}

If any three of the terms are given the fourth one can be found easily.

### Problems on Compound Interest when Interest is Compounded Half-Yearly

1. Find the amount and the compound interest on $12,000 at 8 % per annum for 3 1/2 years if the interest is compounded half-yearly?

Solution:

Given Principal = $12, 000

r = 8% per annum

rate of interest half-yearly = 8/2 %

= 4%

n = 3 1/2

= 7/2 years

when compounded half yearly multiply by 2 i.e. 2n

= 7/2*2

= 7

We know Amount A = P(1+r/100)^{n}

= 12,000(1+4/100)^{7}

=12,000(1+0.04)^{7}

= 12,000(1.04)^{7}

A = Rs. 15791

We know CI = A – P

= 15791 – 12,000

= Rs. 3791

2. Find the compound interest on Rs 5000 for 3/2 years at 5% per annum, interest is payable half-yearly?

Solution:

A = P(1+r/100)^{n}

P = 5000

n = 3/2

2n = 3/2*2

= 3

r = 5%

A = 5000(1+5/100)^{3}

A = 5000(1.05)^{3}

A = Rs. 5788

CI = A – P

= 5788 – 5000

= Rs. 788

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