Question

The Turners have purchased a house for $130,000. They made an initial down payment of $10,000 and secured a mortgage with interest charged at the rate of 4.5%/year on the unpaid balance. (Interest computations are made at the end of each month.) Assume that the loan is amortized over 30 years. (Round your answers to the nearest cent.)

(a) What monthly payment will the Turners be required to make?

$

(b) What will be their total interest payment?

$

(c) What will be their equity (disregard depreciation) after 10 years?

$

Answer 1

Part a:

P = Mortgage Amount = $130,000 - $10,000 = $120,000

r = monthly interest rate = 4.5%/12 = 0.375%

n = 30* 12 = 360 months

Monthly payment = [r*PV] / [1 - (1+r)^-n]

= [0.375% * $120,000] - [1 - (1+0.375%)^-360]

= $450 / 0.740104346

= $608.022374

Therefore, monthly payment required to make is $608.02

Part b:

Total interest paid over life of loan = [360 months * monthly payment] - Mortgage amount

= (360 * $608.02] - $120,000

= $218,887.2 - $120,000

= $98,887.2

Therefore, total interest paid over life of loan is $98,887.2

Part c:

P = Monthly payment = $608.02

r = monthly interest rate = 4.5%/12 = 0.375%

n = 30* 12 = 360 months

x = installments paid = 10*12 = 120 months

Balance of loan after 10 years = P * [1 - (1+r)^-(n-x)] / r

= $608.02 * [1 - (1+0.375%)^-(360-120)] / 0.375%

= $608.02 * 0.592745388 / 0.00375

= $96,106.9469

Equity after 10 years = Mortgament amount - balance after 10 years

= $120,000 - $96,106.9469

= $23,893.0531

Therefore, equity after 10 years is $23,893.05