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%
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.
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