Question

Marilyn knows that she needs $45,000 for a down payment on a house. She found an investment that earns 3.15% interest compounding monthly. She would like to purchase the home in 5 years. How much should she put in the account now to ensure she has her down payment?
$38,450.39

$30,871.96

$44,296.89

$52,665.27


Can you explain how to do it? Thanks :)

Answer 1

She should save $38,450.39.

The formula for the amount of money in an interest-bearing account that is compounded is

$A=p(1+\frac{r}{n})^{nt}$

where A is the total amount in the account, p is the amount of principal invested, r is the interest rate as a decimal number, n is the number of times per year interest is compounded, and t is the number of years.  Using our information we have:

$45000=p(1+\frac{0.0315}{12})^{12\times5} \\ \\45000=p(1.002625)^{60}$

Divide both sides:
$\frac{45000}{1.002625^{60}}=\frac{p(1.002625)^{60}}{1.002625^{60}} \\ \\38450.39=p$