You can afford a $250 per month car payment. You've found a 5 year loan at 6% interest. How big of a loan can you afford?

To determine the size of the loan you can afford based on the monthly payment, interest rate, and loan term, we can use the formula for the present value of an ordinary annuity:

\[
PV = \frac{P \times \left(1 - (1 + r)^{-n}\right)}{r}
\]

Where:
- $ P $ is the monthly payment,
- $ r $ is the monthly interest rate,
- $ n $ is the total number of payments (loan term in months),
- $ PV $ is the present value of the loan (the amount you can afford to borrow).

Given:
- $ P = 250 $ (monthly payment),
- Interest rate = 6% annually → monthly interest rate $ r = \frac{6\%}{12} = 0.005 $,
- Loan term = 5 years → $ n = 5 \times 12 = 60 $ months.

Now, we can plug the values into the formula and calculate:

\[
PV = \frac{250 \times \left(1 - (1 + 0.005)^{-60}\right)}{0.005}
\]

I'll calculate that for you.The size of the loan you can afford, based on a $250 monthly payment for 5 years at 6% interest, is approximately **$12,931.39**.

Do you want more details or have any questions?

Here are five related questions to explore:
1. What happens to the loan amount if the interest rate changes to 7%?
2. How much total interest will you pay over the life of this loan?
3. What would be your monthly payment if you borrowed $15,000 instead?
4. How would a shorter loan term (e.g., 3 years) affect the monthly payment?
5. How does the monthly interest rate affect the loan affordability?

**Tip:** Always compare loan offers from different lenders to find the best interest rate and terms. A small reduction in the interest rate can save you thousands over the life of a loan.

Find out how to calculate the size of a loan you can afford with a $250 monthly payment over 5 years at a 6% annual interest rate. This problem covers financial mathematics concepts such as loan amortization and the present value of annuities. Ideal for students or individuals learning about personal finance and loan calculations.

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