1Finance 550 Practice Problems for Mortgages II

Questions 1-5 Anna Graham has decided to purchase a home in Bethesda, MD. The house is listed for $650,000 and Anna will pay 20% of the price as a down payment and finance the remainder. She has secured a 30-year fixed rate mortgage at 5.4% APR, compounded monthly. However, to get such a good rate, Anna has to pay 1½ points on the amount of her loan. Note: Points are a way to lower your interest rate by agreeing to make an upfront payment. Points are often referred to as origination or discount points and simply represent a fee equal to 1% of the value of the loan. Hence, if you borrow $300,000 and agree to pay half a point, you are charged a fee of $1,500 at closing. Often, the points can be financed which means that they simply increase the amount of your loan by that amount. Thus, in the above case where you borrowed $300,000 and paid half a point, if you financed them, the amount of your mortgage would really be $301,500. 1.What is Anna’s monthly payment? Since Anna will be making fixed monthly payments for a certain length of time, the loan is essentially an annuity. We know that we can determine the monthly payment using the present value of an annuity formula which is: 11(1)tCPVrrWe want to determine the payment which means that we are solving for C. In order to do that, we need to know PV, r, and t. Also recall that C, r, and t MUST match in terms of time periods. Since we are looking for a monthly payment, we need to use a monthly interest rate and number of months. The easiest one of the variables to determine is t – the number of periods. Since the loan is for 30 years and we need to use number of months, t = 360 (30x12). To get r, remember that we are given an annual rate of 5.4% APR, compounded monthly, but we need to get a monthly rate. We ALWAYS want to use the effective period rate. We can solve for the effective period rate using the following: 11mtAPREPRm

2where: APR is the annual percentage rate, m is the number of compounding periods within one year, and t is the number of years in the period we are solving for. Since the rate is compounded monthly, m=12. Remember that the fact that the loan is for 30 years is irrelevant, m is the number of compounding periods within a single year. Since we want to determine the effective monthly rate, we need to determine t. Since t is the number of years in the period we are solving for, we need to determine how many years are in one month. While this may seem like a strange way to describe it, the answer is simply 1/12. Hence, the effective monthly rate is: 112*1210.054111210.004510.0045Eff Month RateThe effective monthly rate is 0.0045. Notice that since APR is by definition, the rate per period multiplied by the number of compounding periods, we could have gotten this another way: