How much could a person borrow for a house if they know they can make a payment of $1030 a month and can get a mortgage for 25 years at 5.10%?

To calculate how much a person can borrow based on a monthly mortgage payment, interest rate, and loan term, we can use the formula for the present value of an annuity, which applies to fixed monthly mortgage payments:

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

Where:
- $ P $ is the loan amount (the principal or amount that can be borrowed).
- $ M $ is the monthly payment ($1030).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments (loan term in months).

Given:
- Monthly payment, $ M = 1030 $
- Annual interest rate = 5.10%, so the monthly rate $ r = \frac{5.10\%}{12} = \frac{0.051}{12} $
- Loan term = 25 years, so the total number of payments, $ n = 25 \times 12 = 300 $ months.

Now, let's calculate the loan amount.

The amount a person can borrow for the house, given the monthly payment of $1,030, a 25-year mortgage at 5.10%, is approximately **$174,449**.

Would you like more details on how this was calculated, or have any further questions?

Here are 5 related questions for further exploration:
1. How does the interest rate affect the total loan amount you can borrow?
2. What would the loan amount be if the mortgage term were only 20 years?
3. How much total interest would be paid over the 25-year term?
4. What is the impact of making extra payments each month on the loan term?
5. How does a change in credit score affect the interest rate on a mortgage?

**Tip:** Making even small extra payments towards your principal can significantly reduce the amount of interest paid over the life of the mortgage.

Find out how much you can borrow for a house if you can afford a monthly mortgage payment of $1030 at a 5.10% interest rate over 25 years. Learn the key concepts of present value of annuities, loan amortization, and interest rates with a detailed step-by-step calculation. Suitable for high school students in Grades 10-12.

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