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Samuel borrows $9,417 from Eric for 9 years. If the annual compound interest rate on the loan is 3.9%, how much will Samuel have to repay at the end of the loan?

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Final answer:

Samuel would have to repay approximately $13,359.16 after borrowing $9,417 at a 3.9% annual compound interest rate over 9 years.

Step-by-step explanation:

Calculating Compound Interest

To calculate the total amount Samuel will have to repay at the end of the 9-year loan with a compound interest rate of 3.9%, we'll use the formula for compound interest:
A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount ($9,417)
r = the annual interest rate (decimal) (0.039)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed (9)

Assuming the interest is compounded annually (n = 1), we calculate:

A = $9,417(1 + 0.039/1)^(1*9)

A = $9,417(1 + 0.039)^9

A = $9,417(1.039)^9

A = $9,417 * 1.418365

A = $13,359.16 approximately

Therefore, at the end of the 9 years, Samuel would have to repay approximately $13,359.16. This example clearly shows that compound interest results in a higher amount compared to simple interest especially with larger sums of money and over longer periods of time, as shown in Step 8.

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