A wealthy benefactor wants to make a donation to a charity that will provide the charity with annual income of $$250,000$ forever, with the first payment to the charity made exactly $20$ years from today. Assume that money donated to the charity will be invested in an account that earns $5\%.$ How large must the donation be to generate the desired income stream?

Answer: The equation for a perpetuity tells us that the present value today equals that cash payment made one year from today divided by the discount rate. In this case, the first payment doesn't come a year from today, but rather $20$ years from today. So if we apply the perpetuity equation, it would give us the present value of the income stream one year before the stream starts, i$.$e$.,$ year $19.$ So the PV of the perpetuity as of today is