Question

Mr. Homemaker has just taken out a $175,000 mortgage at an interest rate of 3.6% [Annual rate]. The mortgage calls for equal monthly payments for 15 years. Then the amount of the monthly payment is:[Assume monthly compounding]

Answer 1

Here, the payments will be same every month, so it is an annuity. We will use the present value of annuity formula to calculate the monthly payments as per below:

PVA = P * (1 - (1 + r)-n / r)

where, PVA = Present value of annuity = $175000, P is the periodical amount, r is the rate of interest = 3.6% compounding monthly, so monthly rate = 3.6% / 12 = 0.3% and n is the time period = 15 * 12 = 180 months.

Now, putting these values in the above formula, we get,

$175000 = P * (1 - (1 + 0.3%)-180 / 0.3%)

$175000 = P * (1 - ( 1+ 0.003)-180 / 0.003)

$175000 = P * (1 - ( 1.003)-180 / 0.003)

$175000 = P * (1 - 0.58321952698) / 0.003)

$175000 = P * (0.41678047301 / 0.003)

$175000 = P * 138.926824338

P = $175000 / 138.926824338

P = $1259.6559

So, the amount of monthly payment is $1259.66