You can afford a $450 per month car payment. You've found a 5 year loan at 3% interest. How big of a loan can you afford?

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To determine how big of a loan you can afford, we will use the formula for the present value of an annuity, which is often used in loan calculations. The formula is:

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

Where:
- $ PV $ is the present value or loan amount (what we are solving for),
- $ P $ is the monthly payment, $ P = 450 $,
- $ r $ is the monthly interest rate, which is the annual rate divided by 12, so $ r = \frac{3\%}{12} = 0.0025 $,
- $ n $ is the total number of payments, which is 5 years multiplied by 12 months, $ n = 5 \times 12 = 60 $.

Now let's calculate the loan amount:

\[
PV = 450 \times \frac{1 - (1 + 0.0025)^{-60}}{0.0025}
\]

\[
PV = 450 \times \frac{1 - (1.0025)^{-60}}{0.0025}
\]

Using the values and simplifying:

\[
PV = 450 \times \frac{1 - 0.8607}{0.0025}
\]

\[
PV = 450 \times \frac{0.1393}{0.0025}
\]

\[
PV = 450 \times 55.72 = 25,073.66
\]

So, the maximum loan you can afford is approximately **$25,073.66**.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does the length of the loan term affect the loan amount you can afford?
2. What would happen if the interest rate were higher, say 5% instead of 3%?
3. How does making larger monthly payments reduce the total interest paid over the life of the loan?
4. What is the formula for calculating monthly payments for different loan amounts?
5. How do early repayments affect the total cost of the loan?

**Tip**: When comparing loans, always consider both the monthly payment and the total interest you'll pay over the life of the loan.

You can afford a $450 per month car payment. You've found a 5 year loan at 3% interest. How big of a loan can you afford?

Calculate the maximum loan you can afford with a $450 monthly car payment over 5 years at 3% interest. Learn about loan calculations using the present value of an annuity formula and the impact of interest rates and loan terms.

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