A mortgage company offers a loan for 30 years at an
annual rate that is equal to the prime rate published by
the Federal Reserve plus 2%. This can be modeled
using the function APR(P) = p + 0.02, where p is the
prime interest rate as a decimal. The annual interest
rate is then converted to a monthly interest rate using
the function (APR) =
APR
The Wilsons want to borrow
12
$128,000. Their monthly payments can be calculated
128,000r
by the function m(r) =
1-(1 + r)-360

Answer: C

Step-by-step explanation:

The Wilsons' monthly mortgage payment will be approximately $9,485.16.

To calculate the monthly payments for the Wilsons' mortgage, we need to follow these steps:

Convert the annual interest rate to a monthly interest rate using the formula APR(P) = P + 0.02.

Plug the monthly interest rate into the formula m(r) = 128,000 * (r / (1 - (1 + r)⁽⁻³⁶⁰⁾)).

Let's perform the calculations:

Step 1: Convert the annual interest rate to a monthly interest rate

Let's assume the prime interest rate (P) published by the Federal Reserve is 4.5% (0.045 as a decimal).

APR(P) = P + 0.02

APR(0.045) = 0.045 + 0.02

APR(0.045) = 0.065 (monthly interest rate as a decimal)

Step 2: Calculate the monthly payments (m(r)) for a loan of $128,000 with the monthly interest rate (r) obtained from Step 1.

m(r) = 128,000 * (r / (1 - (1 + r)⁽⁻³⁶⁰⁾))

m(0.065) = 128,000 * (0.065 / (1 - (1 + 0.065)⁽⁻³⁶⁰⁾))

Now, let's calculate the monthly payments (m(r)):

m(0.065) = 128,000 * (0.065 / (1 - (1 + 0.065)⁽⁻³⁶⁰⁾))

m(0.065) = 128,000 * (0.065 / (1 - (1.065)⁽⁻³⁶⁰⁾))

m(0.065) = 128,000 * (0.065 / (1 - 0.124823)) (Approximately, (1.065)⁽⁻³⁶⁰⁾ ≈ 0.124823)

m(0.065) = 128,000 * (0.065 / 0.875177)

m(0.065) = 128,000 * 0.074285 (Approximately, 0.065 / 0.875177 ≈ 0.074285)

m(0.065) = 9,485.16

The Wilsons' monthly mortgage payment will be approximately $9,485.16.

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