Andy is considering taking a loan to remodel his kitchen. He is offered a loan by his bank for five years and an annual interest of 6.5% with monthly payments. To the nearest 
100, what is the maximum amount of money he can borrow if he can only afford to pay back 
200 per month?

To solve this problem, we need to calculate the maximum loan amount Andy can borrow based on the given monthly payment, interest rate, and loan term.

### Key Information:
- **Monthly Payment ($ P $)**: \$200
- **Annual Interest Rate**: 6.5%
- **Loan Term**: 5 years
- **Payments per year**: 12 (monthly)

### Step 1: Convert the annual interest rate to a monthly interest rate.
The monthly interest rate is calculated by dividing the annual interest rate by 12:
\[
r = \frac{6.5\%}{12} = \frac{0.065}{12} = 0.0054167 \ (\text{monthly interest rate})
\]

### Step 2: Calculate the total number of payments.
The total number of payments over 5 years is:
\[
n = 5 \times 12 = 60 \ (\text{monthly payments})
\]

### Step 3: Use the loan formula to calculate the present value (loan amount).
The loan formula for monthly payments is given by:
\[
PV = P \times \frac{1 - (1 + r)^{-n}}{r}
\]
where:
- $ PV $ is the present value (the loan amount),
- $ P $ is the monthly payment,
- $ r $ is the monthly interest rate,
- $ n $ is the total number of payments.

Now we can substitute the values and calculate the loan amount.

\[
PV = 200 \times \frac{1 - (1 + 0.0054167)^{-60}}{0.0054167}
\]

Let's calculate this.The maximum amount of money Andy can borrow, to the nearest \$100, is **\$10,200**.

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

Here are five related questions to explore:
1. How would the loan amount change if the interest rate increased to 7.5%?
2. What if Andy could afford a monthly payment of \$250 instead of \$200?
3. How does extending the loan term to 6 years affect the loan amount?
4. What is the total interest paid over the 5-year period?
5. How would the loan amount change if payments were made quarterly instead of monthly?

**Tip:** Increasing the loan term reduces the monthly payment but increases the total interest paid over the life of the loan.

Andy is considering taking a loan to remodel his kitchen. He is offered a loan by his bank for five years and an annual interest of 6.5% with monthly payments. To the nearest 100, what is the maximum amount of money he can borrow if he can only afford to pay back 200 per month?

Find out how to calculate the maximum loan Andy can borrow with a 6.5% annual interest rate, a loan term of 5 years, and monthly payments of $200. This guide walks you through the loan amortization formula, interest rate conversion, and calculating present value, making it ideal for students learning basic finance and loan calculations.

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