14 The e Smithsdecide to buy a house priced at 300000 With t

14. The e Smithsdecide to buy a house priced at $300,000. With the $20,000 accumulated from their sinking fund account and another S 10 000 from. savings, they make a 10% down payment and take out a loan on the balance at 8% compounded monthly for the next 30 years. a) Determine the amount of their monthly payments. b) What would be the total interest paid over the 30 years? c) After living in their home for 10 years, they found it necessary to relocate due to Mr. Smith\'s job. Find the unpaid balance of the loan at this time.

Solution

a) The amount of monthy payments,

= P*R*(1+R)^n)/((1+R)^n-1)

P-principal = (300000-30000) = 270000

R-interest rate = 0.08/12 = 0.00667

n=no of monthly payments = 12*30 = 360 months

=270000*(0.00667*(1+0.00667)^360)/(((1+0.00667)^360)-1)

= $1982

b) The total interest paid would be

1982*360-270000 = 443520

c) The formula = 1982*(1-(1+0.00667)^-(10*12))/(0.00667) = $163330.92

So in 10 years 270000-163330.92 = 106669.08 will be paid up and 163330.92 needs to be paid up