Question

Bright Inc. will be receiving $5,500 at the end of every month for the next 4 years. If these payments were directly invested into a fund earning 7.00% compounded semi-annually, what would be the future value of the fund at the end of 4 years?

Answer 1

Periodic Monthly annuity for next 4 years = $5500

Interest rate = 7% compounded Semi-annually

First, Calculating Nominal Interest rate compounded monthly from compounded quarterly using Effective ANnual rate(EAR)formula:-

Where,

r1 = Interest rate compounded semi-annually = 7%

m1 = no of times compounding in a year = 2 (compounded semi-annually)

r2 = Interest rate compounded semi-annually

m2 = no of times compounding in a year = 12 (compounded monthly)

Taking 12-root on both sides,

r2 = 6.90%

So, Nominal Interest rate compounded monthly is 6.90%

Now, Calculating the Future Value at the end of 4 years:-

Where, C= Periodic Payments = $5500

r = Periodic Interest rate = 6.90%/12 = 0.575%

n= no of periods = 4*12 = 48

Future Value = $303,032.36

So, future value of the fund at the end of 4 years is $303,032.36

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