Question

Mary Beth Jones is saving for her retirement fund. She wants to have $550,000 in 25 years when she turns 75. She expects the APR to be 2.6% compounded weekly.
a) How much should she deposit each week?

Answer 1

For that problem use savings plan formula:

$$F = PMT \cdot \frac{(1+\frac{r}{n})^{nt} - 1}{\frac{r}{n}}$$

where

F = Future value,

PMT = Periodic payment,

r = Annual percentage rate (APR) changed to a decimal,

t = Number of years,

n = Number of payments made per year,

$PMT = F[\frac{\frac{r}{n}}{(1+\frac{r}{n})^{nt} - 1}]$ .

So, we have $r= 0.026,$

$n = 52,$

$t=25,$

$PMT = 550000 * [\frac{0.026/52}{(1+0.026/52)^{52*25} - 1}] \approx 300.$

Answer: $300.