TVM - Annuity due Help on Practice Problem
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 correct answer is C$2,221.58.
Draw a time line.
Recognize that the payments in Years 18, 19, 20, and 21 are the future values of a lump sum of C$7,000 in Year 0.
With r = 5%, use the formula for the future value of a lump sum (Equation 2), FVN = PV (1 + r)N, four times to find the payments. These future values are shown on the time line below.
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
- 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.
on Most Calculators
for This Problem
n/a (= 0)
In summary, the couple will need to put aside C$2,221.58 each year if they start next year and make 17 equal payments.
Is there a more time efficient way of doing step 4 in a calculator? I am using Texas BI BAII Plus.
Does one have to find all the FV of the $7000 & then find the PV of these at t17 ?
I am really struggling to understand this Solution.
Study together. Pass together.
Join the world's largest online community of CFA, CAIA and FRM candidates.