Question

how to fine the rate with semi annual compounding

Answer 1

In order to find the semi annual compounding rate, we use the same compound interest formula which is used to find the amount with compound interest.

Formula of compound interest :

Amount= principal × (1+r)^n

In order to find semiannual rate , we divide the rate(r) by 2 , and multiply the time(n) by 2.

For example: - let, Amount= 1,000 ; Principal= 800 ; Time= 1

A= P × (1+r/2)^n×2

1,000 = 800 (1+r/2)^1×2

1,000/800 = (1+r/2)^2

1.25 = (1+r/2)^2

Square root both side

√1.25 = (1+r/2)

1+r/2 = 1.118

r/2 = 1.118 - 1

r/2 = 0.118

r= 0.118 × 2

= 0.236 or 23.6%

In this case, semiannual rate is r/2 i.e. 11.8% and annual rate is r = 23.6%