Here we have annual payments, so we need to use an annual interest rate and annual number of
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.
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.
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%
Thus, the present value of all of the donor’s gifts is $75,9