To determine how much Jeremy owes on his mortgage after the 87th payment, we will use the following approach:

Step 1: Monthly mortgage payment calculation

The formula for calculating the monthly mortgage payment (also called the amortized payment) is:

$M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}$

Where:

• $M$ is the monthly mortgage payment
• $P = 230,000$ is the principal (loan amount)
• $r = \frac{0.0825}{12} = 0.006875$ is the monthly interest rate (8.25% annually compounded monthly)
• $n = 30 \times 12 = 360$ is the total number of payments (for a 30-year mortgage)

Now, let's compute the monthly payment $M$.

Step 2: Remaining balance after 87 payments

To calculate the remaining balance after 87 payments, we use the following formula for the balance of a loan after $k$ payments:

$B_k = P (1 + r)^k - M \left( \frac{(1 + r)^k - 1}{r} \right)$

Where:

• $B_k$ is the remaining balance after $k = 87$ payments
• $P$, $r$, and $M$ are as defined above
• $k = 87$

Now let's compute both $M$ and $B_k$.Jeremy's monthly mortgage payment is approximately $1,727.91. After making 87 payments, the remaining balance on the mortgage is approximately $212,614.02.

Would you like further clarification on any part of the solution?

Here are 5 related questions to consider:

1. How would the balance change if the interest rate were lower?
2. What would be the impact of making additional payments on the principal?
3. How does a mortgage's amortization schedule affect the balance over time?
4. What is the total amount Jeremy will pay over the life of the loan?
5. How would the monthly payment change with a different loan term?

Tip: Making extra payments directly toward the principal can significantly reduce the interest paid over the life of the loan.