You can afford a $350 per month car payment. You've found a 3 year loan at 2% interest. How big of a loan can you afford?


To find the size of the loan you can afford, we will calculate the loan's present value based on your monthly payments, interest rate, and loan term. This is a common application of the formula for the **Present Value of an Annuity**:

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

Where:
- $ PV $ is the present value (loan amount),
- $ P $ is the monthly payment,
- $ r $ is the monthly interest rate (annual interest rate divided by 12),
- $ n $ is the total number of payments (loan term in months).

### Given dataTo find the size of the loan you can afford, we will calculate the loan's present value based on your monthly payments, interest rate, and loan term. This is a common application of the formula for the **Present Value of an Annuity**:

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

Where:
- $ PV $ is the present value (loan amount),
- $ P $ is the monthly payment,
- $ r $ is the monthly interest rate (annual interest rate divided by 12),
- $ n $ is the total number of payments (loan term in months).

### Given 
- Monthly payment, $ P = 350 $ USD,
- Annual interest rate, 2%, so the monthly interest rate $ r = \frac{2\%}{12} = 0.0016667 $,
- Loan term = 3 years, which is $ n = 3 \times 12 = 36 $ months.

Now we can plug these values into the formula to find $ PV $.

\[
PV = 350 \times \frac{1 - (1 + 0.001667)^{-36}}{0.001667}
\]

Let me calculate this for you.The maximum loan amount you can afford, based on a monthly payment of $350 over 3 years at a 2% interest rate, is approximately **$12,219.57**.

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

Here are some related questions:
1. How would the loan amount change if the interest rate were higher?
2. What if you could afford a $400 monthly payment instead?
3. How does the loan term (3 years) affect the loan amount?
4. What is the total interest paid over the life of the loan?
5. How would a lump-sum payment partway through the loan affect the total amount owed?

**Tip:** Longer loan terms typically lower your monthly payment but increase the total interest paid.

You can afford a $350 per month car payment. You've found a 3 year loan at 2% interest. How big of a loan can you afford?

Find out how to calculate the maximum loan you can afford based on a $350 monthly payment over 3 years at a 2% interest rate. Learn to apply the Present Value of an Annuity formula and explore related financial concepts like loan amortization and interest calculations.

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