An amount of 10,000 becomes 20,736 in 2 years. If the interest is compounded half-yearly, what is the annual rate of interest?

Explanation

With half-yearly compounding for two years, there are 4 compounding periods. Let the half-yearly rate be r:

10000(1+r)^4=20736.

Thus

(1+r)^4=2.0736.

But

1.2^4=2.0736,

so the half-yearly rate is 20%. The nominal annual rate is therefore:

2×20%=40%.