Question: you want to set aside some money for your friend...
You want to set aside some money for your friend Pip.
(a) You have great expectations for Pip and want to give him $250,000 a year for 20 years. If you’re able to lock in an effective annual nominal interest rate of 8%, how much do you need to put down today if you want the payments to begin next year?
(b) Before signing the documents to set up Pip’s trust, you decide that you’re feeling even more generous. How much do you need to put down today if you want the payments to go on forever, and you want the payment to begin this year instead of next?
(c) Before signing the more generous contract, your banker points out that $250,000 in 20 years won’t have the same purchasing power as $250,000 today. Assuming the inflation rate is 2%, what is the value of $250,000 in 20 years expressed in today’s dollars?
(d) Terrified by inflation, you ask your banker to set up an annuity that will pay Pip the sum of $250,000 today, $255,000 (= $250, 000(1.02)) next year, $260,100 (= $250, 000(1.02)2 ) in two years, ..., and $371,486.85 (= $250, 000(1.02)20) in twenty years. How much will this annuity set you back?
(e) How much more will the annuity in part (d) cost if the payments go on forever (with the payment in year n equal to $250, 000(1.02)n )?