# 4 what is the minimum amount that needs to be in the

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4. What is the minimum amount that needs to be in the savings account at the time of the donor’s death in order to ensure her final wish is fulfilled? (10 points)
5. What is the present value of ALL (including her final wish) of the donor’s gifts? (10 points) 51 0
5 t r 1 g 1 1 g r C PV Here we have annual payments, so we need to use an annual interest rate and annual number of periods. Remember, c, t, and r MUST match. Since the payments start at time 25 and end at time 50, there are 26 annual payments so t=26. Since we need an annual rate and the savings account rate is 6% compounded monthly, we need to use the effective annual rate which we calculated in question 3. Thus, r=0.0617. We also know that the cash flows will grow at a rate of 5% per year so g=0.05. Finally, the value for C should be the first cash flow so it will be \$10,000. 26 10,000 1.05 1 213,951 0.0617 0.05 1.0617 PV The present value of the growing annuity is \$213,951. HOWEVER, the \$500,000 value of the perpetuity is the present value at date 50 while the \$213,951 value of the annuity is the present value at time 24. Remember that the annuity formula assumes that the payments start at the end of the period, thus because the payments start at time 25, the present value of that growing annuity is at time 24. We need to discount each of these sums back to time zero at the annual interest rate which is 6.17% 24 50 213,951 500,000 (1.0617) (1.0617) 50,848 25,054 75,902 PV PV Thus, the present value of all of the donor’s gifts is \$75,9 02
6. How much does the donor need to deposit each month into her savings account in order to fulfill ALL her philanthropic wishes? (10 points)
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