Question

Consider a 30‐year mortgage on at $400,000 house that requires monthly payments and has an interest rate (APR) of 8% per year. You have $ 50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price.  

a) What will your monthly payments be if you sign up for this mortgage?

b) Suppose you sell the house after 10 years. How much will you need to pay off the remaining mortgage at that time (the end of year 10)?

Answer 1

a.

i = 8%/12 = 0.666667%

t = 30*12 = 360 months

loan = 400000 - 50000 = 350000

Monthly loan payment = 350000*(A/P,0.666667%,360)

= 350000*0.00666667*((1 + 0.00666667)^360)/((1 + 0.00666667)^360-1)

= 350000*0.00666667*((1.00666667)^360)/((1.00666667)^360-1)

= 2568.18

b.

No. of monthly payments after 10 yrs = 20*12 = 240

Loan principal remaining to be paid = 2568.18*(P/A,0.666667%,240)

= 2568.18*((1 + 0.00666667)^240-1)/( 0.00666667*(1 + 0.00666667)^240)

= 2568.18*((1.00666667)^240-1)/( 0.00666667*(1.00666667)^240)

= 307036.85