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.