Suppose you are interested in buying a car. If you can afford a monthly payment of 
350, what is the maximum 
3 year loan you can afford 
 1.75% interest?

To determine the maximum loan amount you can afford with a monthly payment of $350 over 3 years (36 months) at an interest rate of 1.75%, we can use the formula for the monthly payment of an amortizing loan:

\[
M = \dfrac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $M$ is the monthly payment ($350 in this case),
- $P$ is the loan principal (the amount we are solving for),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the number of payments (36 months for a 3-year loan).

Let's solve this equation for $P$.

### Step 1: Convert the annual interest rate to a monthly interest rate
\[
r = \dfrac{1.75\%}{12} = \dfrac{0.0175}{12} = 0.00145833
\]

### Step 2: Plug in the known values and solve for $P$
We know that:
- $M = 350$,
- $r = 0.00145833$,
- $n = 36$.

Now, solving for $P$.

Let me calculate this for you.The maximum loan amount you can afford with a monthly payment of $350 over 3 years at 1.75% interest is approximately **$12,266.25**.

Would you like any further details, or do you have any other questions?

Here are 5 related questions to explore:
1. How does the loan term affect the maximum loan amount?
2. What happens if the interest rate increases to 3%?
3. How would the loan amount change with a higher monthly payment?
4. What is the total interest paid over the life of the loan?
5. How can early repayments affect the total loan cost?

**Tip:** When taking out a loan, it’s helpful to calculate both monthly payments and the total cost to ensure it's affordable long-term.

Suppose you are interested in buying a car. If you can afford a monthly payment of 350, what is the maximum 3 year loan you can afford at 1.75% interest?

Find out the maximum car loan you can afford with a $350 monthly payment over 3 years at an interest rate of 1.75%. Learn how to use the loan amortization formula to determine the principal amount and understand the impact of interest rates on loan affordability.

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