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?

Solution:

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), FV__{N}_ = PV (1 + r), four times to find the payments. These future values are shown on the time line below.^{N} *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*. C$62,677=X[(1.06)17−10.06]=28.21288XX=C$2,221.58**Notation Used****on Most Calculators**** Numerical Value ****for This Problem***N*17 %*i*6 PV n/a (= 0) FV C$62,677 PMT**compute***X*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.**