Exponential Functions - Basic Score: $2 / 5$ Penalty: none Question Watch Video Show Examples 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? Answer Attempt 1 out of 2 Submit Answer
Solution
Step 1 ：The problem is asking for the future value of an investment given an initial amount, an interest rate, and a time period. This is a classic application of the formula for compound interest, which is: \(FV = PV * (1 + r/n)^{nt}\) where: \(FV\) = future value, \(PV\) = present value (initial amount), \(r\) = annual interest rate (in decimal form), \(n\) = number of times interest is compounded per year, \(t\) = time in years.
Step 2 ：In this case, the interest is compounded annually (\(n=1\)), the initial amount is $9000, the interest rate is 8% or 0.08, and the time is 17 years. We can plug these values into the formula to find the future value.
Step 3 ：Given: \(PV = 9000\), \(r = 0.08\), \(n = 1\), \(t = 17\)
Step 4 ：Calculate: \(FV = 33300.16249320779\)
Step 5 ：Final Answer: The amount in the account after 17 years, to the nearest cent, will be \(\boxed{33300.16}\).
