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aunt zelda’s son starts college in 5 years for which she will need $15,000 payable at...

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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Answer #1

Annual payment for 4 years = $15,000
Interest rate = 6%

t= 0 1 2 4 7 9 15000 15000 15000 15000

Cost of Annuity 5 years from today = $15,000/1.06 + $15,000/1.06^2 + $15,000/1.06^3 + $15,000/1.06^4
Cost of Annuity 5 years from today = $15,000 * (1 - (1/1.06)^4) / 0.06
Cost of Annuity 5 years from today = $15,000 * 3.465106
Cost of Annuity 5 years from today = $51,976.59

Cost of Annuity today = $51,976.59/1.06^5
Cost of Annuity today = $38,839.93

So, she has to pay $38,839.93 or $38,840 for this annuity

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