Section 8.2 Installment Loans
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Example 8-2C
See It
Kayla has a loan that she used to buy a new computer. She originally
borrowed $1,200 at an annual interest rate of 7.5%. Kayla has been making
monthly payments of $54 and wants to pay her loan off early. There are six
remaining payments, and the principal balance is $317.03. What will be Kayla’s
fi nal payment if she pays the loan off early?
Strategy
Use the formulas:
monthly interest rate =
annual interest rate
number of payments per year
interest due = monthly interest rate × principal balance
early payoff amount = principal balance + interest due
Solution
Step 1: Determine the monthly interest rate. Divide the annual interest rate by
12 (the number of payments per year).
monthly interest rate =
annual interest rate
number of payments per year
monthly interest rate = 0.625%
Step 2: Convert the monthly interest rate to a decimal by moving the decimal
two places to the left.
0.625% → 0.00625
Step 3: Determine the interest due. Multiply the monthly interest rate by the
principal balance. Round to the nearest cent ($0.01) if necessary.
interest due = monthly interest rate × principal balance
interest due = 0.00625 × $317.03
interest due = $1.98
Step 4: Determine the early payoff amount. Add the remaining principal
balance and the interest due.
early payoff amount = principal balance + interest due
early payoff amount = $317.30 + $1.98
early payoff amount = $319.28