Question

You are looking to purchase a new home. You are talking to a lender about a 3.625% interest rate loan for 30 years that amortizes monthly.

What is your mortgage constant?

How to enter your answer? Let's say your calculated answer is 0.02759. That is the same thing as 2.759% so you should enter 2.759 as your final answer. Decimals matter for mortgage constants, interest rates, and cap rates, so don't round this example to 2.8. You need to keep at east two decimal places.

3.625 rate = 5.473% 30 years

please show work thank you

Answer 1

Assume the amount of loan is $100,000.

Compute the monthly interest rate, using the equation as shown below:

Monthly rate = Annual rate/ 12 months

                      = 3.625%/ 12 months

                      = 0.30208333333%

Hence, the monthly interest rate is 0.30208333333%.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

PVIFA = {1 – (1 + Rate)^-Number of periods}/ Rate

                   = {1 – (1 + 0.00302083333)^-360}/ 0.30208333333%

             = 219.273576473

Hence, the present value annuity factor is 219.273576473.

Compute the monthly loan payment, using the equation as shown below:

Loan payment = Loan amount/ Present value annuity factor

                       = $100,000/ 219.273576473

                        = $456.051301796

Hence, the monthly loan payment is $456.051301796.

Compute the mortgage constant, using the equation as shown below:

Mortgage constant = (Monthly payment*12 months)/ Loan amount

                               = ($456.051301796*12 months)/ $100,000

                               = 5.473%

Hence, the mortgage constant is 5.473.