Retirement Problem

An example using annual payments is in Time Value part $3$ starting with slide #$87$

Part $($a$)$: Fill in the table below to determine the amount of your savings at the end of each $5-$year period:

Part $($b$)$: You will retire at the end of year $20$ and move your investments to a safer account that will earn $3\%$ APR per year. If you expect to live for another $20$ years,

what is the maximum amount you could withdraw each month and not run out of money for $20$ years?

The appropriate PVFA for this calculation

You could withdraw a maximum of

$$4,936\mathrm{.}33$ per month.

Part $($c$)$: Suppose it is the end of year $15,$ and you know you want to have an income of $$5,500$ per month in retirement. If you still plan to retire at the end of year $20,$

how much would you have to save per month for the last $5$ years to meet your goal?

Put your answer her

$$2,047\mathrm{.}53$

Part $($d$).$ You decide your answer from part $($c$)$ is too high, so you will seek a higher return. Assuming you will save the original amount per month from years $16-20,$

what rate of return would you have to earn in the last $5$ years to meet your goal? Report this answer as an APR.