A wealthy stockbroker decided, rather late, to set up a college fund for his daughter, exactly one year before graduating from High School. She intended to study medicine and become a Doctor. She figured, it would take her about 7 years to get her MD. Her father decided to invest in a fund called a "REIT." He was certain he could get 10% comp. annually, and the fund would have enough money in it, in one year, to allow his daughter to withdraw $50,000 per annum @ 5% comp. annually, for her tuition fees and her living expenses, for 7 years. He began the fund by depositing an initial amount and then doubled the payment every month thereafter, for 12 payments in total. What was the value of the fund at the end of the year and how much was his initial deposit?. P.S. This is a college-level question in a business course. Any help would be great and many thanks. [REIT, stands for "Real Estate Income Trust"].
The first part of your question is very simple. We simply find the PV of her 7 payments of $50,000 each @ 5% comp. annually=PV=$289,318.67. You use the common TVM formula to calculate this, which is:
PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1=PV OF $1 PER PERIOD.
The second part is a little more involved. However, there is also a TVM formula to calculate it directly, which I'm sure is in your textbook. However, we may not need it in this case. Because, her father's monthly payments double every month for 12 months, then we can solve directly for the first payment. If we put the first payment as P, then we have:
P x 2^12=$289,318.67. Solve for P.
P=$289,318.67 / 2^12
P=$70.63. This should be his first payment minus interest. Since the interest he got was 10% comp. annually, we have to convert this to a monthly compound, which comes to about 9.57%. 9.57/(12 x 100) +1=1.007975. This is the monthly interest rate. We divide the above payment by this and we should get his initial deposit: $70.63/1.007975=$70.08, which is his initial deposit.
