Question

2. Assume that you are buying a house for $500, 000 and you have to finance 80% of it from the bank at 6% p.a. for 20 years. It is to be repaid monthly.

a) What is the monthly repayment amount? Assume the interest is compounded monthly.

b) At the end of year 5 you have to sell your house and move to the U.S.

i. How much money do you still owe the bank?

ii. How much principal and interest have you paid in the last 5 years?

iii. If the house price increases on average 10% per year, how much would you be able to take to the U.S. after selling the house and payoff the loan?

Answer 1

Q-2)

Loan amount = Price of House*80%

= $500,000*80%

= $400,000

a). Calculating the Monthly Payment of Loan:-

Where, P = Loan Amount = $400,000

r = Periodic Interest rate = 6%/12 = 0.5%

n= no of periods = 20 years*12 = 240

Monthly Payment = $2865.72

b). At the end of year 5 you sell the house.

i). Calculating the Outstanidng loan balance after year 5:-

Where, P = Loan Amount = $400,000

r = Periodic Interest rate = 6%/12 = 0.5%

n= no of periods = 20 years*12 = 240

m = no of payments made = 5 years*12 = 60

Outstanding balance = $339,598.69

So, Amount you owe to bank at year end 5 is $339,598.69

ii). Principal repaid in last 5 years = Loan Amount - Outstanding balance at the end of year 5

= $400,000 - $339,598.69

= $60,401.31

Interest repaid in last 5 years = (Monthly payment*No of payments) - Principal repaid in last 5 years

= ($2865.72*60) - $60,401.31

= $111,541.89

iii). Initial house price at the time of Buying = $500,000

Price of house after 5 years with 10% per year increase in price = $500,000*(1+0.10)^5

= $805,255

Outstanding Loan balance at the end of year 5 = $339,598.69

Amount you be able to take to the U.S. after selling the house and payoff the loan = $805,255 - $339,598.69

= $465,656.31