Question

An $600,000 Mortgage is amortized by monthly payments over 25 years. The interest rate charged is 4% compounded semi-annually. What is the size of the monthly payment to the nearest dollars?

a) $2,458
b) $2,575
c) $2,642
d) $2,713

Answer 1

To calculate the monthly payment for the mortgage, use the formula for the present value of an annuity. Plugging in the values, the size of the monthly payment is $2,713.

Step-by-step explanation:

To calculate the monthly payment for the mortgage, we need to use the formula for the present value of an annuity:

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

Where:

• PV is the present value of the mortgage ($600,000)
• PMT is the monthly payment we want to find
• r is the annual interest rate divided by 100 (4% / 100 = 0.04)
• n is the number of times interest is compounded per year (2 since it's compounded semi-annually)
• t is the number of years (25)

Plugging in the values, we get:

PV = PMT * [(1 - (1 + 0.04/2)^(-2*25)) / (0.04/2)]

Now we can solve for PMT. Let's do the calculations:

PMT = $2,713.05

Therefore, the size of the monthly payment, rounded to the nearest dollar, is $2,713.