A life insurance company pays investors 5 compounded annuall

A life insurance company pays investors 5% compounded annually on its five-year GICs. For you to be indifferent as to which compounding option you choose, what would the nominal rates have to be on GICs with quarterly compounding? Interim calculations should be to 5 decimal places; final answer to the nearest .01%

Solution

For calculating future value compounding annually of single cash flow.

Fv=pv(1+r)ⁿ

Where , r=rate of interest

n=no of year(GICS) , fv= future value , pv= present value

Given, rate of interest=5%. No of years=5years

Now if LIC is compounded annually then

Fv=pv(1+5/100)⁵ = 1.27628*pv

However if it is compounded quarterly then

Fv=pv(1+r%/4)^n*4

Therefore , Fv=pv(1+5/400)^5*4 = 1.28204* pv

That is since there is 4 quarter in a year therefore interest will be compounded 4 times in a year. therefore , rate will be divided by 4 and no of years will be multiplied by 4 respectively.