Sample Problem 1: Mortgage Payments
In this lecture, we will look at how to solve our first real math question. And we will use the big six to do it. Let’s get right to it. Here is our question. You would like to buy a condo in North Vancouver. You are looking to get a mortgage with a 20 year amortization period for $430,000. The interest rates are currently j12 = 4.5%. How much are your monthly payments? Let’s solve this using the Big Six. First, let’s look at what we know and if the compounding frequency matches the payment frequency in this case. Our interest rate is j12 = 4.5%, so the compounding frequency is 12 times a year, or monthly. Payments are also monthly. This means that our compounding and payment frequencies match and we can use the Big Six without the NPEPN. Take a piece of paper and write down the big six like I have it on the screen: I/YR, P/YR. N. PV, FV, and PMT. Now let’s read the question again and write what we know: II’YR is 4.5. P/YR is 12, N is our amortization period. It is 20 years. But remember we don’t write it as 20, we write it in compounding periods, so 20years x 12 compounding periods per year = 240. We will use the borrower’s perspective in this case because for most people it’s more intuitive to think as a borrower than to think as a bank. PV is how much you borrow, will are using the borrower's perspective so the PV is positive, 430,000. Because the borrower gets 430, 000 from the bank. FV is how much you will owe the bank at the end of your mortgage. Well, the way mortgages work is you pay them off over the years, so you will owe nothing after 20 years. Your mortgage will be paid off. The FV is 0. This will always be the case with mortgages. At the end of your amortization period you owe nothing, the mortgage is paid off. FV is 0. Now for payment, we don’t know what it is, the question is asking for it. So I will put a question mark here. Great, now we have 5 out of 6 Bix Six values, so we can find the sixth one – the payment. The way we are going to do this is enter everything we know into our calculator, and then after we enter the 5 values we can press payment key to see what the payment is. Let’s walk through the steps. You can pull out your calculator if you’d like and follow along. Interest rate is 4.5%, so I type 4.5 and press I/YR. This saves the value 4.5 in the I/YR key. Then I type 12 and press SHIFT P/YR. This saves 12 in the P/YR key. \Type 240 and press N, 430,000 and press PV, 0 and press FV. Now we have entered all 5 values into the calculator. Note that we didn't have to do it in this exact order, but I recommend that you always write the Big Six in the same order and enter the values from top to bottom to avoid any mistakes. Now I just press PMT and see -2,720.39231775 on the screen. The payment is negative because as a borrower, You are making the payment to the bank every month, giving the money away. We could have solved this question from the bank’s perspective, in which case the PV would be negative, and the payments would be positive. I suggest doing mortgage questions from the borrower’s perspective, because it’s more intuitive to think as a borrower than to think as a bank (unless you are a banker, of course). Note that you cannot pay the bank 2720.39231 cents, so the payment is always rounded up to the next higher cent, unless the questions specifies otherwise. In this case, our rounded payment is $2,720.40. That’s our final answer.