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William's son starts college in 16 years

Finance

William's son starts college in 16 years. He estimates the current deficit for his college education funds is $74,990. Assume that after-tax rate of return that William is able to earn from his investment is 9.61 percent annually. He is going to invest additional amounts every month at the beginning of the period for 7 years. Compute the monthly beginning of-the-period payment that is necessary to fund the current deficit. (Please use monthly compounding, not simplifying average calculations).

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Computation of Monthly beginning of-the-period payment using PMT Function in Excel:

=pmt(rate,nper,-pv,fv,type)

Here,

PMT = Monthly beginning of-the-period payment = ?

Rate = 0.7676%

Nper = 7 years*12 months = 84 months

PV = 0

FV = $74,990

Type = 1 (at the beginning)

Substituting the values in formula:

=pmt(0.7676%,84,0,-74990,1)

PMT or Monthly beginning of-the-period payment = $634.08

 

Workings:

Computation of Monthly Rate of Return:

Monthly Rate of Return = (1+r)^(1/n) - 1

= (1+9.61%)^(1/12) - 1

= 1.007676 - 1

Monthly Rate of Return = 0.007676 or 0.7676%

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