Question

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)= The Wilsons want to borrow
$128,000. Their monthly payments can be calculated
by the function m(r):
128,000
1-(1+r)-360

Answer 1

M = $128,000 * [(p + 0.02) / 12] * [1 + (p + 0.02) / 12]^360 / [[1 + (p + 0.02) / 12]^360 - 1]

Explanation:

If you must know how to solve it

The monthly payment for a mortgage can be calculated using the formula:

M = P * r * (1 + r)^n / [(1 + r)^n - 1]

where M is the monthly payment, P is the loan amount, r is the monthly interest rate, and n is the number of months.

In this case, the Wilsons want to borrow $128,000. We can use the given function APR(p) = p + 0.02 to find the annual interest rate. If p is the prime interest rate as a decimal, then the annual interest rate is APR(p) = p + 0.02.

To convert the annual interest rate to a monthly interest rate, we use the function:

(APR) / 12

So we have:

APR(p) / 12 = (p + 0.02) / 12

Now we can substitute this expression for r in the mortgage payment formula:

M = P * [(p + 0.02) / 12] * [1 + (p + 0.02) / 12]^360 / [[1 + (p + 0.02) / 12]^360 - 1]

where n = 360 since there are 30 years in the loan term.

Substituting P = $128,000 into this formula gives:

M = $128,000 * [(p + 0.02) / 12] * [1 + (p + 0.02) / 12]^360 / [[1 + (p + 0.02) / 12]^360 - 1]

Answer 2

c

Explanation: