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Answer :
The interest rate refers to the fee charged by the lender, expressed as a percentage of the total amount borrowed. The effective interest rate is 8.30% (rounded to two decimal places).
The effective interest rate is the actual amount paid by the borrower on a loan. The formula for effective interest rate is:
Effective interest rate formula
Effective interest rate = [(1 + i / n)^n - 1] x 100
Where i is the interest rate and n is the number of compounding periods in a year.
Month-end payments of \( \$ 1,430 \) are made to settle a loan of \( \$ 138,940 \) in 9 years.
Using the formula for the effective interest rate and substituting the given values:
Effective interest rate = [(1 + i / n)^n - 1] x 100138940
= 1430[(1 + i / 12)^12 x 9 - 1]138940 / 1430
= (1 + i / 12)^12 x 9 - 1[math]\frac{138940}{1430}+1[/math]
= (1+i/12)^12 * 9[math]\sqrt[12]{\frac{138940}{1430}}[/math]
=1+i/12i = 12[math]\left(\sqrt[12]{\frac{138940}{1430}}-1\right)[/math]i
≈ 0.6645
Effective interest rate ≈ [(1 + 0.6645/12)^12 - 1] x 100
Effective interest rate ≈ 8.30%
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