In this problem there are repeated regular payments into an account to save money. The formulas we will use assume all the payments are the same size, compounding happens at the same time the payments are made, and the interest rate stays constant. Even if these things are not perfectly true, such as when you are only guessing at a rate of return, these formulas may be used to predict the answer. Even though some answers are predictions, round each answer to the nearest penny.
The formulas for this problem are the first two in the Ordinary Annuity section of the formula page. Notice that they have an A for the final amount of savings in the account and the letter M for the regular repeated payment. Either of the two formulas work for each problem but the easiest one to use is the one that has the variable you are trying to find by itself at the beginning of the equation. If you use the equation that has the variable you want inside the formula, you will need to use a little algebra.
Annual percentage rate is a measure of the power of an account. When interest is compounded, the interest rate is actually more effective than it looks. Annual percentage rate, also called effective rate or annual yield, is a measure of that effectiveness. Compare that to wind chill where the temperature may actually be 23 degrees Fahrenheit but it feels like 12 degrees. With the heat index, it may be 89 degrees Fahrenheit but feel like 94. An athlete may be 6 feet 9 inches but block like they were 7 feet 2 inches. In finance, an account may be 4% but have an effective rate of 4.074% due to compounding. The annual percentage yield answers should look like the annual rate given but be a little higher. Round to 3 decimal places.
A couple wants to save $20,000 for the down payment on a house. They make monthly payments for 7 years into an account paying 3.0% compounded monthly.
A. What is the size of their monthly payment?
B. How much interest will they earn?
C. What is the annual percentage yield?
annual % is 3. There monthly % is 3/12 = 0.25%
total periods = 7years X 12months = 84 periods
To get montlhy payment we have to divide future value required by future value annuity factor of 0.25%, 84 periods
Size of monthly payment = FV/FVAF(0.25%,84) = $20000/93.34* = $212.902
*FVAF calculated from FVAF table
Total cash outflow = 84 periods X $212.902 monthly payments = $17,883.768
Total future value = $20,000
Total Interest they will earn = $20,000 – 17,883.768 = $2,116.232