You decide to borrow $23 000 to do some renovations on your home Monthly payments for three years at 2.5% financing compounded monthly.

To calculate the monthly payments for a loan of $ \$23,000 $ over three years at an annual interest rate of $ 2.5\% $ compounded monthly, we can use the formula for the monthly payment on an installment loan:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal loan amount (\$23,000).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments (loan term in months).

First, we convert the annual interest rate to a monthly interest rate:

\[ r = \frac{2.5\%}{12} = \frac{0.025}{12} = 0.002083 \]

Next, we calculate the total number of payments over three years:

\[ n = 3 \text{ years} \times 12 \text{ months/year} = 36 \text{ months} \]

Now we can substitute these values into the formula:

\[ M = \frac{23000 \cdot 0.002083 \cdot (1 + 0.002083)^{36}}{(1 + 0.002083)^{36} - 1} \]

Let's calculate it step-by-step:

1. Calculate $ (1 + r)^n $:

\[ (1 + 0.002083)^{36} \approx 1.077304 \]

2. Calculate the numerator:

\[ 23000 \cdot 0.002083 \cdot 1.077304 \approx 51.6145 \]

3. Calculate the denominator:

\[ 1.077304 - 1 = 0.077304 \]

4. Finally, divide the numerator by the denominator:

\[ M = \frac{51.6145}{0.077304} \approx 667.63 \]

Therefore, the monthly payment is approximately $ \$667.63 $.

Would you like more details or have any questions?

Here are 5 questions you might consider next:
1. How is the total interest paid on the loan calculated?
2. What would be the monthly payment if the interest rate were higher or lower?
3. How does the length of the loan term affect the monthly payment and total interest paid?
4. What are the implications of compounding interest monthly versus annually?
5. How can you compare different loan offers effectively?

**Tip:** When planning to take out a loan, consider using an online loan calculator to quickly compare different loan terms and interest rates to find the best option for your financial situation.

Learn how to calculate monthly payments for a $23,000 loan over three years at a 2.5% annual interest rate, compounded monthly. This detailed calculation uses the installment loan formula, covering key financial concepts. Suitable for adults looking to understand loan repayment calculations.

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