Final answer:
The amount financed for the computer purchase with monthly payments of $30 over three years at an 18% annual interest rate is $855.23. The total interest cost over the three years is $224.77.
Step-by-step explanation:
Calculating the Installment Contract for a Computer Purchase
To calculate the amount financed and the interest cost for the purchase of a computer, we will use the formula for the present value of an annuity because the payments are made at regular intervals. Given an interest rate of 18% per annum compounded monthly, and payments of $30 at the end of each month for three years (36 months), we need to calculate the present value of these payments to find the amount financed.
The present value (PV) of an annuity formula is:
PV = PMT * [(1 - (1 + i)^-n) / i]
Where PMT is the monthly payment, i is the monthly interest rate (annual interest rate divided by 12), and n is the total number of payments.
Substituting the given values:
i = 18% / 12 = 1.5% = 0.015
n = 3 years * 12 months/year = 36 months
Using a calculator:
PV = $30 * [(1 - (1 + 0.015)^-36) / 0.015]
PV = $30 * [(1 - (1.015)^-36) / 0.015]
PV = $30 * [28.50776447]
PV = $855.23
The amount financed, therefore, is $855.23. To calculate the total interest cost, we need to find the total amount paid over the three years and subtract the amount financed from it.
Total Payments = Monthly Payment * Number of Payments
Total Payments = $30 * 36 = $1,080
Interest Cost = Total Payments - Amount Financed
Interest Cost = $1,080 - $855.23 = $224.77
So, the total interest cost is $224.77.