You are so excited about buying your first house but you mus

You are so excited about buying your first house, but you must take out a mortgage for $175,000. (a) What will the monthly payment be if the length of mortgage is 30 years and the interest rate is 6.5%? (b) How much interest will you pay over the life of the loan? (c) Suppose that you can only afford monthly payments of $1000 per month. What interest rate must you now obtain to get the same house?

Solution

1.a) The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is   P = L[r(1 + r)ⁿ]/[(1 + r)ⁿ - 1]. Here, L = 175000, r = (6.5/100)*1/12 = 13/2400 and n = 30*12 = 360. Then, P =175000*(13/2400)*[(1+13/2400)³⁶⁰]/ [(1+13/2400)³⁶⁰-1] = (11375/12)[ (2413/2400)³⁶⁰]/ [(2413/2400)³⁶⁰-1] =(11375/12)* 6.991797982/5.991797982 = $1106.12 (on rounding off to the nearest cent). Thus, the monthly payment will be $1106.12.

(b) The interest paid over the life of the loan will be $ 1106.12 *360 - $ 175000 = $ 398203.20-$175000 = $ 223203.20.

(c) If one can afford to pay only $100 per month, then on using a mortgage calculator, the rate of interest that is to be asked for is 5.558% instead of 6.5%.