Answer:(a) To find the amount owed after one year on a loan with compound interest, you can use the formula for compound interest:
\[A = P \times \left(1 + \frac{r}{n}\right)^{nt}\]
Where:
- \(A\) = Amount owed after \(t\) years
- \(P\) = Principal amount (initial loan amount)
- \(r\) = Annual interest rate (in decimal form)
- \(n\) = Number of compounding periods per year
- \(t\) = Number of years
Given:
- Principal (\(P\)) = $7,400
- Annual interest rate (\(r\)) = 9.6% or 0.096 (in decimal form)
- Compounding periods per year (\(n\)) = 4 (quarterly compounding)
- Time (\(t\)) = 1 year
Plug in the values into the formula:
\[A = 7400 \times \left(1 + \frac{0.096}{4}\right)^{4 \times 1}\]
Calculate the exponent and compute the amount owed (\(A\)).
The amount owed after one year will be $________ (rounded to the nearest cent).
(b) To find the effective annual interest rate (EAR), you can use the formula:
\[EAR = \left(1 + \frac{r}{n}\right)^n - 1\]
Where:
- \(r\) = Annual interest rate (in decimal form)
- \(n\) = Number of compounding periods per year
Given:
- Annual interest rate (\(r\)) = 9.6% or 0.096 (in decimal form)
- Compounding periods per year (\(n\)) = 4 (quarterly compounding)
Plug in the values into the formula and calculate the EAR.
The effective annual interest rate, expressed as a percentage, will be ________% (rounded to the nearest hundredth of a percent).
Explanation: