Question

One hundred identical mortgages are pooled together into a pass-through security. Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly), and is fully amortized over a term of 30 years. What is the monthly payment on the mortgage pass-through

Answer 1

The monthly payment on the mortgage pass-through is $110,064.69.

Step-by-step explanation:

The monthly payment on the mortgage pass-through can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = M * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value or principal of the pass-through = 100 * $150,000 = $15,000,000

P = Monthly payment on the mortgage pass-through = ?

r = monthly interest rate = fixed annual interest rate / 12 = 8% / 12 = 0.08 / 12 = 0.00666666666666667

n = number of months = 30 years * 12 months = 360

Substitute the values into equation (1) and solve for M, we have:

$15,000,000 = M * ((1 - (1 / (1 + 0.00666666666666667))^360) / 0.00666666666666667)

$15,000,000 = M * 136.283494133963

M = $15,000,000 / 136.283494133963

M = $110,064.69

Therefore, the monthly payment on the mortgage pass-through is $110,064.69.