Jeremy takes out a 30-year mortgage of 230000 dollars
at an annual interest rate of 6.5 percent compounded
monthly, with the first payment due in one month. How
much does he owe on the loan immediately after the 87th
payment?

To determine how much Jeremy owes on his mortgage after the 87th payment, we need to use the **mortgage loan formula** to first calculate the monthly payment and then the remaining balance after the 87th payment.

### Step 1: Monthly Payment Formula
The formula for calculating the monthly mortgage payment $ M $ is:

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

Where:
- $ P $ is the principal loan amount (in this case, $230,000),
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the total number of payments (30 years × 12 months = 360 payments).

First, calculate the monthly interest rate:

\[
r = \frac{6.5\%}{12} = \frac{0.065}{12} \approx 0.00541667
\]

Now we can calculate the monthly payment $ M $:

\[
M = 230,000 \times \frac{0.00541667(1 + 0.00541667)^{360}}{(1 + 0.00541667)^{360} - 1}
\]

### Step 2: Remaining Loan Balance Formula
The formula for calculating the remaining balance $ B $ after $ k $ payments is:

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

Where:
- $ P $ is still the loan amount ($230,000),
- $ r $ is the monthly interest rate (0.00541667),
- $ n $ is the total number of payments (360),
- $ k $ is the number of payments made (87).

I will now compute the monthly payment and then the remaining balance after the 87th payment.Jeremy's monthly mortgage payment is approximately **$1,453.76**. After making the 87th payment, the remaining balance on the loan is approximately **$206,970.07**.

Would you like further details or explanations on any part of the process?

Here are five related questions you might be interested in:
1. How can we calculate the total interest paid over the life of the mortgage?
2. How would the monthly payment change if the interest rate were lower?
3. What would be the impact of making extra payments towards the principal?
4. How is the loan affected if the term is reduced to 15 years instead of 30?
5. What if Jeremy refinances the loan after making 87 payments?

**Tip**: When considering mortgage payments, paying a bit extra toward the principal each month can significantly reduce the total interest paid over the life of the loan.

Jeremy takes out a 30-year mortgage of 230000 dollars at an annual interest rate of 6.5 percent compounded monthly, with the first payment due in one month. How much does he owe on the loan immediately after the 87th payment?

Learn how to calculate the remaining loan balance on a 30-year mortgage of $230,000 after 87 payments at an annual interest rate of 6.5% compounded monthly. This solution uses the amortization formula to determine monthly payments and the remaining balance. Suitable for high school and college students.

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