Anthony and Michelle Constantino just got married and received $35:000 in cash g

Question

Anthony and Michelle Constantino just got married and received $35:000 in cash gifts for their wedding. Use your financial calculator or the Money in Motion calculator (which is available in MyFinanceLab) to determine how much will they have on their twenty-fifth anniversary if they place half of this money in a fixed-rate investment earning 16 percent compounded annually. Would the future value be larger or smaller if the compounding period was 6 months? How much more or less would they have earned with this shorter compounding period? If they place half of this money, PV, in a fixed rate investment earning 16 percent compounded annually, the amount they will have, FV, on their twenty-fifth anniversary is $ (Round to the nearest cent.)

Explanation / Answer

Calculation of future value of the fund invested (Compounding annually):

Future value = Present value * ( 1+ rate )^ years

= (35000/2) ( (1+16%) ^25

= $715299.27

Hence value of total fund at the end of 25 years   = 715299.27 + (35000/2)

= $732799.27

Calculation of future value of the fund invested (Compounding semiannually):

Future value = Present value * ( 1+ rate/2 )^ (years*2)

= (35000/2) ( (1+16%/2) ^(25*2)

= $820778.22

Hence value of total fund at the end of 25 years   = 820778.219+ (35000/2)

= $838278.22

Hence difference in using the compounding time = $838278.22 -$732799.27 =$105478.95

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