Final answer:
Using the loan amortization formula, the monthly payment for Neil's 25-year $84,000 loan at 7% interest is calculated to be approximately $564.99, which does not match any of the options provided.
Step-by-step explanation:
The size of the monthly installment for Neil's 25-year $84,000 loan at 7% interest can be calculated using the formula for an amortizing loan, commonly referred to as the fixed installment for an installment loan. To find the monthly payment, we use the formula:
M = P * [i(1 + i)^n] / [(1 + i)^n - 1]
where:
- M is the total monthly payment
- P is the principal loan amount ($84,000)
- i is the monthly interest rate (7% per year divided by 12 months)
- n is the number of payments (25 years * 12 months)
First, we calculate the monthly interest rate:
i = 7% per annum / 12 = 0.07 / 12 ≈ 0.00583333
Then we calculate the number of payments:
n = 25 years * 12 months = 300
Now, inputting these into the formula, we get:
M = $84,000 * [0.00583333(1 + 0.00583333)^300] / [(1 + 0.00583333)^300 - 1]
After performing the calculations, we find the monthly payment to be approximately $564.99, which is not listed in the provided options. Hence, it appears there might be an error with the options given or with the provided loan terms.