# Aunt Zelda’s son starts college in 5 years for which she will need \$15,000 payable at the end of each of the 4 years. Suppose she can buy an annuity in 5 yrs. that will enable her to make the four \$15,000 annual payments. Draw a timeline for all cash flows. What will be the cost of the annuity 5 years from today? What is the most she should be willing to pay for it if purchased today? Assume an interest (discount) rate of 6% during these 9 years.

Question

Aunt Zelda’s son starts college in 5 years for which she will need \$15,000 payable at the end of each of the 4 years. Suppose she can buy an annuity in 5 yrs. that will enable her to make the four \$15,000 annual payments. Draw a timeline for all cash flows. What will be the cost of the annuity 5 years from today? What is the most she should be willing to pay for it if purchased today? Assume an interest (discount) rate of 6% during these 9 years.

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Step 1

Aunt Zelda will buy an annuity at the beginning of year 5 that will pay \$15000 for college at the end of year 5, end of year 6, end of year 7 and end of year 8 ( beginning of year 9).

Periodic payments of \$15000 will constitute annuity of 4 years at 6%.

Present Value of Annuity (for year 5) can be calculated using formula for PV of future annuity  given by:

PV = Annual Payments * [ 1 - (1+ rate)^-n]/ rate

PV =\$15000 * [1 -(1+6%)^-4]/ 6%

PV = \$15000*[1- 1.06^-4]/0.06

PV ( at year 5) = \$51976.5842

Step 2

To calculate the present value of annuity at year 0, we must discount it at 6% for 5 years

Present value of annuity ( at year 0) = Annuity Value ( year 5)/ (1 + rate) ^5

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