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

Answer:

She needs $6,949.65 in the account today.

Step-by-step explanation:

The compound interest formula is given by:

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

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.

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

$9000 = P(1 + \frac{0.09}{1})^{1*3}$

$P(1.09)^{3} = 9000$

$P = \frac{9000}{(1.09)^{3}}$

$P = 6949.65$

She needs $6,949.65 in the account today.