Question

John and Katie bought a house in Edmonton exactly 7 years ago. They took out a mortgage of $500,000 at that time. The mortgage has a 25-year amortization period, monthly mortgage payments, and a quoted interest rate of 5% (APR, semi-annually compounded).

John and Katie recently decided to buy a new house, also in Edmonton. Today they will receive payment from the buyer of their old home and make a down payment on the new house. If the old house sold for $700,000, the new one is priced at $900,000, and the down payment on the new house equals the net proceeds from the sale of their old house, how big is their new mortgage (assuming monthly mortgage payments)? (Net Proceeds = Selling Price of the old House – Outstanding Principal Balance on the old Mortgage).

Select one:

a. $454,472

b. $455,726

c. $615,762

d. $615,274

e. $520,000

f. $200,000

g. $642,538

h. $697,889

NOTE: Please show all the work, not using EXCEL. (Step by step with equations) Thanks!

Answer 1

Interest rate=5% APR , semi annually compounded.

Semi-annual interest rate =(5/2)=2.5%

Monthly interest=r

(1+r)^6=(1+0.025)

1+r=1.025^(1/6)= 1.004124

r=1.004124-1=0.004124

Monthly interest rate=0.4124%=0.004124

Number of months of amortization =25*12=300

Monthly Payment:

CAF=Capital recovery Factor =(A/P,i,N)=(i*((1+i)^N))/(((1+i)^N)-1)

i=0.004124,N=300

CAF=(A/P,0.004124,300)=(0.004124*(1.004124^300))/((1.004124^300)-1)= 0.005816

Monthly Payment =$500,000*CAF=$500,000*0.005816=$2,908

Present value of seven years payment:

PWF=Present Worth Factor (P/A,i, N)= (((1+i)^N)-1)/ (i*((1+i)^N))

i=0.004124

N=7*12=84

PWF=(P/A, 0.004124,84)= (((1+i)^N)-1)/ (i*((1+i)^N))= ((1.004124^84)-1)/ (0.004124*(1.004124^84))= 70.8724076

Present Value of seven years payment=70.8724076*$2908=$206,101

Outstanding Loan at Present Worth =$500,000-$206101=$293,899

Outstanding Loan at end of seven years=$293,899*(1.004124^84)= $415,274

Selling Price of old house=$700,000

Amount in hand (net proceeds)after paying off old house balance=$700,000-$415,274=$284,726

Down Payment for the new house=$284,726

Loan amount for new house=$900,000-$284,726=$615,274

ANSWER:

d. $615,274