Question

7. You want to buy a house and will need to borrow $280,000. The interest rate on your loan is 6.19 percent compounded monthly and the loan is for 20 years. What are your monthly mortgage payments?

Answer 1

Formula for Equal monthly payment (EMI) is:

EMI = P × r × (1 + r) ⁿ /{(1 + r)ⁿ - 1 }

Where,

P = Principal= $ 280,000

r = rate of interest = 6.19 % or 0.0619/12 p.a. or 0.005158333 monthly

n = No. of periods = 20 years x 12 months = 240 periods

Equal monthly payment = $ 280,000 x 0.005158333 x (1 + 0.005158333)²⁴⁰ / {(1 + 0.005158333) ²⁴⁰ -1}

= $ 280,000 x 0.005158333 x (1.005158333)²⁴⁰ / {(1.005158333) ²⁴⁰ -1}

= $ 280,000 x 0.005158333 x 3.437752551/ (3.437752551-1)

= $ 280,000 x 0.005158333 x 3.437752551/ (2.437752551)

= $ 280,000 x 0.005158333 x 1.410213908

                        = $ 2036.818954 or $ 2,037

Monthly mortgage payment is $ 2,037.