Final answer:
To find out if the monthly payment for a $26,000 car loan at a 5% interest rate over four years is affordable, we use the loan payment formula. If the resulting monthly payment is at most $650, the car is affordable. Interest and other costs should also be considered when budgeting for a car.
Step-by-step explanation:
To determine whether you can afford a car with a sticker price of $26,000 by making monthly payments of $650 for four years, we need to calculate the total amount that will be paid over the term of the loan including interest. Given that the credit union has agreed to loan the money at an annual interest rate of 5%, we can use the formula for calculating monthly loan payments, which is derived from the annuity formula.
Monthly Payment Calculation
The formula for the monthly payment (M) is:
M = P [i(1+i)^n] / [(1+i)^n – 1]
Where:
- P is the principal amount of the loan ($26,000),
- i is the monthly interest rate (annual rate/12),
- n is the total number of payments (4 years * 12 months/year).
Converting the annual interest rate to monthly gives us:
i = 5% / 12 = 0.0041667
And the total number of payments, n, is:
n = 4 * 12 = 48
Substituting these values into the formula gives us the monthly payment amount. After calculating, if the resulting monthly payment is less than or equal to $650, the car is affordable under these terms.
It is crucial to remember that over the term of a loan, you will pay more than the principal amount due to interest charges. It is also important to consider additional costs such as insurance, maintenance, and taxes when considering the affordability of a vehicle.