Final answer:
The amount financed for an installment contract of a car can be calculated using the present value of an annuity formula, which considers monthly payment, interest rate, and the total number of payments.
Step-by-step explanation:
To calculate the amount financed for a car using an installment contract, we will use the present value of an annuity formula. Since the payments are made at the end of each month, we are dealing with an ordinary annuity. This means the formula to use is:
PV = PMT [1 - (1 + i)^{-n}] / i,
where PV is the present value (amount financed), PMT is the monthly payment, i is the monthly interest rate, and n is the total number of payments.
In this case, PMT is $226.76, the monthly interest rate i is 4% per annum compounded monthly which gives us 0.04/12 per month, and n is 2.75 years times 12 months/year, totaling 33 payments. Plugging the values into the formula, we can calculate the amount financed.