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Abdul took out a loan for $7,400 that charges an annual interest rate of 9.6%, compounded quarterly. Answer each part. (a) Find the amount owed after one year, assuming no payments are made. Do not round any intermediate computations, and round your answer to the nearest cent.

(b) Find the effective annual interest rate, expressed as a percentage.
Do not round any intermediate computations, and round your answer to the nearest hundredth of a percent.

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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:

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