You can afford a $300 per month car payment. You've found a 4 year loan at 5% interest. How big of a loan can you afford?

To calculate how large of a loan you can afford with a $300 per month payment on a 4-year loan at 5% interest, we can use the formula for the present value of an ordinary annuity. The formula is:

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

Where:
- $PV$ = Present Value (loan amount)
- $P$ = Monthly payment ($300)
- $r$ = Monthly interest rate (annual rate divided by 12, so $ \frac{5\%}{12} = 0.004167$)
- $n$ = Total number of payments (4 years × 12 months = 48 payments)

Let's calculate the loan amount.

\[
PV = 300 \times \frac{1 - (1 + 0.004167)^{-48}}{0.004167}
\]

I will calculate this now.The largest loan you can afford, given a $300 per month payment over 4 years at 5% interest, is approximately **$13,026.89**.

Would you like further details or have any questions about this calculation?

Here are 5 related questions to explore:
1. How would the loan amount change with a different interest rate?
2. What if you increased the loan term to 5 years instead of 4 years?
3. How much total interest would you pay over the 4-year period?
4. How much would the monthly payment be for a loan of $15,000 under the same conditions?
5. What effect does increasing the monthly payment have on the loan amount?

**Tip:** Longer loan terms reduce monthly payments but increase the total interest paid.

You can afford a $300 per month car payment. You've found a 4-year loan at 5% interest. How big of a loan can you afford?

Discover how to calculate the maximum loan amount you can afford with a $300 monthly payment over a 4-year period at 5% interest. This problem covers key financial concepts such as present value of annuities and interest rate calculations, suitable for Grades 10-12.

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