Harry borrowed $1,800 for two years at 13% a year under an
add-on plan. He repaid the loan, including interest, in 24 equal
payments. How much was each payment?
The first thing I wonder is how was interest compounded?
To find out how much each payment is, we can use the formula for calculating payments under an add-on plan. In an add-on plan, the interest is added to the principal loan amount, and the total is then divided by the number of payments.
The formula for calculating payment under an add-on plan is:
Payment = (Principal + Total Interest) / Number of Payments
Let's break down the steps to find how much each payment is:
Step 1: Calculate the total interest paid over the loan period.
Total Interest = Principal x Interest Rate x Loan Period
In this case, Principal = $1,800, Interest Rate = 0.13 (13% expressed as a decimal), Loan Period = 2 years.
Total Interest = $1,800 x 0.13 x 2 = $468
Step 2: Calculate the total amount to be repaid.
Total Amount = Principal + Total Interest
Total Amount = $1,800 + $468 = $2,268
Step 3: Calculate the amount of each payment.
Each Payment = Total Amount / Number of Payments
In this case, Number of Payments = 24 (repaid in 24 equal payments).
Each Payment = $2,268 / 24 ≈ $94.50
Therefore, each payment that Harry needs to make is approximately $94.50.