Question 7 (10 points) The Johnson family is worried about their ability to pay college tuition for their daughter Chloe. Tuition rates are currently $9,500 per year at the state college and have been increasing at a rate of 7% annually. Chloe will begin college in 7 years. The Johnson’s have $9,500 set aside now in a college plan that will earn 6% per year. They recently heard about a plan to pre-pay tuition at current rates, that is pay $9,500 per year of college. Should they pre-pay Chloe’s first year now or keep the money invested and pay the tuition 7 years from now? How much are they saving in FV terms with this decision? Don't Pre-pay; 781 Don't Pre-pay; 685 Pre-pay; 970 Pre-pay; 685 Pre-pay; 781 Don't Pre-pay; 970 We don’t need to make any calculations in order to determine which option is better, the right option to choose is of course pre-pay, what we need to find now is how much they will save in choosing this option. 1,07 7 − 1 × 9.500$ = ( 1 + 0,009 ) × 9.500$ = 1,0097 × 9.500$ = 1,065 × 9.500$ = 10.114,9$ 1+ 1,06 ( 10.114,9 − 9.500 ) $ = 614,9$ There isn’t any option equal to this solution but the nearest one is 685, so Pre-pay; 685 will be the right option. 7
Question 8 (15 points) Ralph knows that he is going to have to replace his roof soon. If he has the roof replaced now, it will cost $10,000. He could wait 5 years, but it will then cost him $20,000. At what rate will these options cost the same. (Hint: This is also known as the break-even point. Exact calculation up to two decimals is not difficult. If stuck, trial and error will help. (No more than two decimals in the percentage interest rate but do not enter the % sign.) Answer for Question 8
In order to find at what interest the options will be equal we must calculate at what rate money doubles after five years, so we must do: 20.000$ 5 = 2 = 1,1487 10.000$ 1,1487 − 1 = 0,1487
14,87% The interest rate at which the options will be equal is 14,87€....