Suppose a bank decides to make a mortgage loan to an individual so that they may purchase a home. The homeowner will pay the bank $1500 per month in mortgage payments for the next 30 years. The bank will collect the mortgage payments at the end of the month. What is this promised stream of cash flows worth to the bank today if they could reinvest the monthly income at an annualized rate of 5% for the entire investment horizon?

Question

Quizplus · Accepted Answer

To calculate the present value (PV) of the mortgage payments, we need to use the formula for present value of an annuity:

PV = PMT x [(1 - (1 + r)^-n) / r]

Where:
PMT = $1500 (monthly payment)
r = 5%/12 = 0.004166667 (the monthly interest rate)
n = 30 x 12 = 360 (the total number of payments)

Plugging in the numbers:

PV = $1500 x [(1 - (1 + 0.004166667)^-360) / 0.004166667]
PV = $279,422.43

Therefore, the promised stream of cash flows is worth $279,422.43 to the bank today if they could reinvest the monthly income at an annualized rate of 5% for the entire investment horizon.

Suppose a Bank Decides to Make a Mortgage Loan to an Individual