In a previous example, Helen and Harold Nash planned to make 17 identical payments to fund the college education of their daughter, Susan. Alternatively, imagine that they planned to increase their payments at 4 percent per year. What would their first payment be?

The first two steps of the previous Nash family example showed that the value today of the college costs was $9,422.92. These two steps would be the same here. However, the third step must be altered. Now we must ask: How much should their first payment be so that if payments increase by 4 percent per year, the present value of all payments will be $9,422.92?

We set the growing annuity formula equal to $9,422.92 and solve for C:

Here, C = $1,192.75. The deposit on their daughter’s first birthday is $1,192.75, the deposit on the second birthday is $1,240.46 (= 1.04 × $1,192.75), and so on.

Transcribed Image Text:

17 1+g 1.04 1. 1 (1 [¹-(:)]- [¹ - )" 1+r) 1.14 = $9,422.92 .14.04 r-g