321.3
Austin Danger Powers was cryogenically frozen for 30 years. Assume that he had savings totaling $50,000 when he was frozen. If his money was invested at 10% for the 30 years he was frozen (from 1967 to 1997), how much of an annual cash flow (an annuity) could he fund starting in 1998 and lasting for 25 years? Assume a return of 10% per year throughout this problem. (2 pts)
This is another one where you really need to draw a cash flow diagram:
1967 … 1997 1998 … 2022 50,000 0 FV CF … CF The initial investment of $50,000 will grow through the interest it accrues over 30 years at 10% per year. In 1997, it will grow to: $872,470.11 which comes from: FV=PV(1+r)^n = $50,000 (1.10)^30.
Now, this is the amount of money that Austin will have to fund his annuity for the next 25 years. If we want to know what CF he can withdrawal each year for 25 years, then we use the annuity formula to solve for the cash flows:
\( \LARGE CF = \frac{872{,}470.11} { \left [ \frac{1}{.10} - \frac{1}{.10 \left (1+.10 \right )^{25}} \right ] } = 96{,}118.35 \)