Question

Graded Problem Set Jenna needs to make some house repairs in three years that will cost $9,000. She has some money in an account earning 9% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs

Answer 1

She needs $6,949.65 in the account today.

Explanation:

The compound interest formula is given by:

`A(t) = P(1 + (r)/(n))^(nt)`

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

In this question:

She needs $9,000 in 3 years, so
`t = 3, A(t) = A(3) = 9000`

9% annual interest, so
`r = 0.09`

1 compounding, so
`n = 1`

How much money needs to be in the account today so she will have enough to pay for the repairs

We need to find P.

`A(t) = P(1 + (r)/(n))^(nt)`

`9000 = P(1 + (0.09)/(1))^(1*3)`

`P(1.09)^(3) = 9000`

`P = (9000)/((1.09)^(3))`

`P = 6949.65`

She needs $6,949.65 in the account today.