Question

In: Finance

what must have been the interest rate per annum if $32421780.75 is earned as the future...

what must have been the interest rate per annum if $32421780.75 is earned as the future value after investing $12500000 for five years at a bank compounded semiannually.

please provide step by step working

Solutions

Expert Solution

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%.


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