In: Finance
Future Value = $32,421,780.75
Present Value = $12,500,000
Interest compounding = semi-annual
Period = 5 years or 10 semi-annuals (5 years * 2 semiannuals in a year)
Let Semi-annual interest rate be X
As per Time Value of Money equations,
Future Value = Present Value * (1+Rate)^Period
= $32,421,780.75 = $12,500,000*(1+X)^10
= $32,421,780.75/$12,500,000 = (1+X)^10
= 2.59374 = (1+X)^10
= 2.59374^(1/10) = (1+X)
= 1.10 = 1+X
=1.10-1 = X
=X = .10 or 10%
Thus, semi annual interest rate = 10%
Annual Percentage Rate = 10%*2 = 20%
Since, it is compoundng semi-annually, Effective Annual Rate = ((1+10%)^2)-1 = 21%.