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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