Hi everyone, there is a question from the curriculum that I don’t know how to do.
Q: A couple plans to pay their child’s college tuition for 4 years starting 18 years from now. The current annual cost of college is C$7,000, and they expect this cost to rise at an annual rate of 5 percent. In their planning, they assume that they can earn 6 percent annually. How much must they put aside each year, starting next year, if they plan to make 17 equal payments?
The solution is as follow:
Step 1 : Draw a timeline and calculate the future value of the college tuition from t= 18 to t = 21 which is the sum of the following cash flows: ( I get this part)
7000(1.05)^18 = 16846
7000(1.05)^19 = 17689
7000(1.05)^20 = 18573
7000(1.05)^21 = 19502
Step 2 : Using the formula for the present value of a lump sum (r = 6%), equate the four college payments to single payments as of t = 17 and add them together. C$16,846(1.06)−1 + C$17,689(1.06)−2 + C$18,573(1.06)−3 + C$19,502(1.06)−4 = C$62,677*
Step 3 : Equate the sum of C$62,677 at t = 17 to the 17 payments of X , using the formula for the future value of an annuity (Equation 7). Then solve for X .
I am currently stuck in step 2. Can someone please explain why an interest rate of 6% is used instead of 5%?Isn’t 5% the annual growth rate of the tuition cost ? I know we need to calculate the present value of the lump sum at t= 17 but I don’t get why 6%is used instead of 5%.
Thanks in advance!!!