Question

Mark Hamilton purchased a brand new condo in downtown Vancouver for a Mortgage value of $160,000. Mark was able to make the 20% required down payment in order to avoid mortgage insurance. At the time, the rate of the mortgage is a 25‐year fixed-rate mortgage at 8.340%, compounded semi-annually.

1) Using Present Value of Annuity formula, find Mark's monthly Payment at the beginning of the Annuity?

2) How much has mark paid towards his condo in 8 Years?

Answer 1

1.
rate compounded monthly r=((1+rate compounded semi annually/2)^(2/12)-1)*12=((1+8.34%/2)^(2/12)-1)*12=8.1986795261%

Monthly payment=Price*(1-downpayment%)*(rate/12)/(1-1/(1+rate/12)^(12*t))=160000*(1-20%)*(8.1986795261%/12)/(1-1/(1+8.1986795261%/12)^(12*25))=1004.830353

2.
Loan oustanding=160000*(1-20%)*(1+8.1986795261%/12)^(12*8)-1004.830353/(8.1986795261%/12)*((1+8.1986795261%/12)^(12*8)-1)=110404.68

Loan paid=Price*(1-downpayment%)-Loan outstanding=160000*(1-20%)-110404.68=17595.32