We have a 1,000,000 dollars in our savings and we are trying to decide if we should use our cash buy an apartment or go with a mortgage fixed for five years. We only have these two options, no mixed option available.

We know that the five year mortgage compound interest rate given by the banks today is 4.5%per year, meaning that we will pay $246,181.94 of interest by the end of the period, the interest will be divided equally in the five years of the mortgage. We checked in the powerful oracle of Google, that the projected inflation rate for Canada in the next five years is 3.5% a year average.

The bank offers a 5% compound interest rate if we invest our money for five years with them giving $276,281.56 cad at the end of the period. The bank will pay 55,256.31 of our interests each year.

I am going to save $12,000 a year as I wont pay rent, though the cost of owning the apartment will be $5,000 Cad a year today (this number will increase every year due to inflation).

What I want you to tell me, is how much will the loan will cost me at the end of the period, we are trying to find the cost of a loan when I have a million dollars invested at 5% for five years.

You need to do two discounted cash flows, one with the mortgage, this should give you a decreasing in time negative value as the dollar that you are paying today is not going to have the same value of the dollar paid in the 5^th year, this is the present value of the interests that you will pay in five years. The other one is the discounted cash flow of your investment, it will tell you the present value of how much that million dollars is going to produce in five years, then you just need to get the difference between the total earned from your investment in five years and the total paid for the mortgage in five years, and that will be your cost of the money!