Question

How much would you need to deposit in an account now in order to have $3000 in the account in 15 years? Assume the account earns 8% interest compounded monthly.

Answer 1

To solve this problem, we will use the formula for monthly compounded interest:

$T=P(1+\frac{r}{12})^{12t},_{}$

where:

- T is the final amount,

- P is the initial amount,

- r is the annual interest rate,

- t is the number of years.

Substituting T=3000, t=15, and r=0.08, we get:

$3000=P(1+\frac{0.08}{12})^{12\times15}.$

Solving the above equation for P we get:

$P=\frac{3000}{(1+\frac{0.08}{12})^{12\times15}}=907.19.$

Answer:

$907.19$

dollars.