Question

in 15 years Pam hope to have $30,000to make a down payment on a house. how much would she need to invest right now in a mutual fund that earns 8% annual interest in order to have enough for her down payment in 15 years​

Answer 1

She needs to invest $13,636.36 right now

Explanation:

This is a simple interest problem.

The simple interest formula is given by:

`E = P*I*t`

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

`T = E + P`

In this question:

In 15 years, so
`t = 15`

She wants to have $30,000, so
`T = 30000`

8% interest, so
`I = 0.08`

We have to find P.

`T = E + P`

`30000 = E + P`

`E = 30000 - P`

Replacing:

`E = P*I*t`

`30000 - P = P*0.08*15`

`30000 - P = 1.2P`

`2.2P = 30000`

`P = (30000)/(2.2)`

`P = 13636.36`

She needs to invest $13,636.36 right now