Sample Problem 2: Mortgage Payments with NPEPN
In this lecture, we will solve another sample question, this time a little more complex. And we will use the big six to do it. Let’s start. Here is the question. You would like to buy a condo in Vancouver. You are looking to get a mortgage with a 25 year term and amortization period for $550,000. The interest rates are currently j2 = 5%. How much are your monthly payments? Let’s solve this using the Big Six. First, let’s look at if the compounding frequency matches the payment frequency in this case. Our interest rate is j2 = 5%, so the compounding frequency is 2 times a year, or semi-annually. Payments, on the other hand, are MONTHLY. This means that our compounding and payment frequencies DO NOT MATCH and we need to do the interest rate conversion using the NPEPN. Let’s take a piece of paper and write down the big six. Because we need the NPEPN in this case, we will cross out the I/YR and P/YR and do the NPEPN instead. Here I wrote down what NPEPN stands for in case you have not yet memorized it. Now let’s read the question again and write what we know: The rate is given to us as j2=5%, so I’m going to write it down in the first part of my NPEPN. We want the compounding frequency to match the payment frequency, which is monthly, so I’m going to write down 12 as the P/YR I want. N is our amortization period. It is 25 years. But remember we don’t write it as 25, we write it in compounding periods, so 25 years x 12 compounding periods per year = 300. PV is how much you borrow, will use the borrower's perspective and write it as positive 550,000. FV is how much you will owe the bank at the end of your mortgage. The 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. Now let’s do this on the calculator. I suggest you take your calculator and follow me as we go along. We start with the NPEPN. Interest rate is 5%, so I type 5 and press SHIFT Nom. Then I type 2 and press SHIFT P/YR. Press SHIFT Effective. Then I type 12 and press SHIFT P/YR. And press SHIFT NOM. This is our interest rate converted to J12. We don’t need to write it down, just proceed with the Big Six starting with the N. Type 300 and press N, 550,000 and press PV, 0 and press FV. Now I just press PMT and see -3,198 on the screen. Remember that we always have to round the payment to the next higher cent, unless the questions specifies otherwise. In this case, our payment is $3,198.83 That’s our final answer.