Question

You are buying a property costing of $750,000 by taking a mortgage to cover the entire purchase price. The nominal interest rate is 6% per annum compounded monthly. The bank offers 3 options for the structure of the repayments.

Option 3: Month-end-instalments of $Y will be made for the first 5 years. Then the bank offers you a payment free period (i.e., no repayments required) of 5 years. After that, the remaining balance will be repaid over 15 years by month-end-instalments of $Y. e) Calculate Y.

Answer 1

Loan oustanding after 5 years=Loan*(1+periodic rate)^n-onthly payment/periodic rate*((1+periodic rate)^n-1)=750000*(1+6%/12)^(12*5)-Y/(6%/12)*((1+6%/12)^(12*5)-1))

Loan oustanding after 10 years=present value*(1+periodic rate)^n=(750000*(1+6%/12)^(12*5)-Y/(6%/12)*((1+6%/12)^(12*5)-1))*(1+6%/12)^(12*5)

Present value of Monthly payments starting from year 10 will be equal to loan outstanding after 10 years

(750000*(1+6%/12)^(12*5)-Y/(6%/12)*((1+6%/12)^(12*5)-1))*(1+6%/12)^(12*5)=Y/(6%/12)*(1-1/(1+6%/12)^(12*15))

=>Y=6417.99