Answer:
$315,717.03
Explanation:
Let us start by first of determining the future value of $50,000 quarterly payments for 16 years using the future value of an ordinary annuity provided below:
FV=quarterly payment*(1+r)^n-1/r
quarterly payment=$50,000
r=quarterly interest rate=8%/4=2%
n=number of quarterly payments in 16 years=16*4=64
FV=$50,000*(1+2%)^64-1/2%
FV=$50,000*(1.02)^64-1/0.02
FV=$50,000*(3.551493243
-1)/0.02
FV=$50,000*2.551493243
/0.02
FV=$6,378,733.11
The future value above fell short of the target $7,500,000, it means a fixed amount would have to be invested at 8% compounded quarterly for 16 years as well
shortfall=$7,500,000-$6,378,733.11=$1,121,266.89
The present value of the shortfall that would be invested today is computed
PV=FV/(1+r)^n
FV=$1,121,266.89
r=quarterly interest rate=2%
n=number of quarters in 16 years=64
PV=$1,121,266.89/(1+2%)^64
PV=$315,717.03
