Question

9000 dollars is placed in an account with an annual interest rate of 8%. how much will be in the account after 17 years, to the nearest cent?

Explanation:

Step1: Determine the formula

We use the compound - interest formula \(A = P(1 + r)^t\), where \(A\) is the amount of money accumulated after \(t\) years, including interest, \(P\) is the principal amount (the initial amount of money), \(r\) is the annual interest rate (in decimal form), and \(t\) is the time the money is invested for in years.
First, we need to convert the annual interest rate from a percentage to a decimal. The annual interest rate \(r = 8\%=0.08\), the principal \(P=\$9000\), and the time \(t = 17\) years.

Step2: Substitute the values into the formula

Substitute \(P = 9000\), \(r=0.08\), and \(t = 17\) into the formula \(A=P(1 + r)^t\).
We get \(A=9000\times(1 + 0.08)^{17}\).
First, calculate \((1 + 0.08)^{17}\). Using a calculator, \((1.08)^{17}\approx3.700018\).
Then, multiply this by the principal: \(A = 9000\times3.700018\approx33300.16\)

Answer:

\(\$33300.16\)