Question

29) The Johnsons have $45,000 saved for their son's college fund. They invest the money in anaccount that earns 7.5% interest, compounded yearly. If f(x) = 45,000(1.075) represents theamount of money in the account after x years, how much money will be in the account after 7years?

Answer 1

SOLUTION:

Case: Compound interest

Given:

Amount saved: $45,000

Interest rate: 7.5%

Compound interest model: Amount, f(x) is such that:

$f(x)=45000(1.075)^x$

Where x is the number of years after investments

Required: how much money will be in the account after 7 years?

Method:

Step1: Recreate the model

$f(x)=45,000(1.075)^{x}$

Step 2: Plug the value of x=7 in the model

$\begin{gathered} f(x)=45,000(1.075)^{x} \\ f(7)=45,000(1.075)^7 \\ f(7)=74657.21 \end{gathered}$

Final answer:

After 7 years, there will be $74657.21 in the account