Question

Sabrina has decided to invest her savings in real estate. 20 months ago, she purchased a duplex for $800,000. She could afford to make a down-payment of $50,000. The bank gave her a 30-year mortgage with constant monthly payments at a quoted APR of 12% with semi-annual compounding. Today, (after making her last monthly payment to the bank) Sabrina was able to resell her property for $815,000. With the money she has left after paying the bank for the remaining mortgage, Sabrina will make a down-payment on a new property. What is the down-payment she can make on this new property? Hint: First find the monthly payments she must make.

Answer 1

Loan amount = Price of Duplex - Down payment = $800,000 - $50,000

= $750,000

Quoted APR = 12% semi-annual compounding

Calculating the APR compounded monthly from semi-annual compounding using EAR formula:-

where, r1 = Interest rate compounded monthly

m1 = no of times compounding in a year = 12

r2 = Interest rate compounded semi-annually = 12%

m2 = no of times compounding in a year = 2

Taking 12-root on both sides,

r1 = 11.710548%

So, APR compounded monthly is 11.710548%

Now, Calculating the Outstanding Loan Balance today after 20 monthly payments:-

Where, P = Loan amount = $750,000

r = Periodic Interest rate = 11.710548%/12 = 0.975879%

n= no of periods = 30 years*12 = 360

m = no of loan payments already made = 20 months

Outstanding Loan Balance Today = $744,973.65

- Sale Value of property = $815,000

Amount left for down-payment of another property after paying off loan = $815,000 - $744,973.65

Amount left for down-payment of another property after paying off loan = $70,026.35