2. Jon Hamm would like to establish a fund for cancer research at St. Jude Child

Question

2. Jon Hamm would like to establish a fund for cancer research at St. Jude Children's Research Hospital in downtown Memphis, Tennessee. Researchers at the hospital have informed Jon that they would like to receive an additional $10M per year to help them find a cure. Jon has agreed to deposit $8.5M now into a fund that pays interest at 7% per year. He will also deposit $7.5M into the fund five years from now. Eight years from now, Jon will make a deposit $5.5M into the fund and he will continue to deposit money until the fund can support $10M perpetual withdrawals from the fund. Researchers would like to begin withdrawing $10M per year from the fund twenty years from now. Compute the number of years (to two decimal places) that Jon will have to make the $5.5M donations in order for the researchers and Jon to meet their financial objective

Explanation / Answer

Amount of money needed in 20 years

= 10 m / 7% = $142,857,143

Now, the value of $8.5m in 20 years = 8.5 x (1 + 7%)^20 = $32,892,318

Value of $7.5m in 15 years

= 7.5 x (1 + 7%)^15 = $20,692,736

Hence, the additional value required in 20 years

= (142,857,143 - 32,892,318 - 20,692,736)

= $89,272,089

Now, its value in 8 years when Jon would begin making $5.5m annual deposit = 89,272,089 / (1 + 7%)^12 = $39,637,875

Now, no. of years Jon had to make deposit can be calculated using N function

I/Y = 7%, PMT = -5.5 ,

PV = $39,637,875 , FV = 0

Compute N = 10.38 years in order to reach their objective.

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