To find the monthly payment and total interest for a mortgage, we can use the mortgage formula for the monthly payment:

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

where:

• $M$ = monthly payment
• $P$ = principal loan amount ($46,000)
• $r$ = monthly interest rate (annual rate divided by 12)
• $n$ = total number of payments (loan term in months)

Given:

• Principal $P = 46,000$
• Annual interest rate = $5.34\%$ (0.0534 as a decimal)
• Loan term = 40 years

Calculations:

1. Convert the annual interest rate to a monthly interest rate: $r = \frac{0.0534}{12} \approx 0.00445$

2. Calculate the total number of payments: $n = 40 \times 12 = 480$

3. Plug values into the formula: $M = 46000 \times \frac{0.00445(1 + 0.00445)^{480}}{(1 + 0.00445)^{480} - 1}$

4. Calculating $(1 + r)^n$: $(1 + 0.00445)^{480} \approx 6.7510$

5. Now substitute back to find $M$: $M = 46000 \times \frac{0.00445 \times 6.7510}{6.7510 - 1}$ $M = 46000 \times \frac{0.029986}{5.7510} \approx 46000 \times 0.00522 \approx 240.49$

Monthly Payment:

$M \approx 240.49$

Total Payments Over 40 Years:

$\text{Total payments} = M \times n = 240.49 \times 480 \approx 115,836.80$

Total Interest:

$\text{Total interest} = \text{Total payments} - P = 115,836.80 - 46,000 \approx 69,836.80$

Final Answers:

• Monthly payment: $240.49 (rounded to the nearest cent)
• Total interest: $69,836.80

Would you like to go into more detail on any part of the calculation? Here are some related questions you might consider:

1. How would the monthly payment change with a different interest rate?
2. What would the total interest be for a shorter loan term?
3. How does making extra payments affect the total interest?
4. What are some factors that can influence mortgage rates?
5. How do you calculate the effective interest rate if fees are included?

Tip: Always compare different mortgage offers, as even a small difference in the interest rate can lead to significant changes in total payments and interest.