Suppose you are a carefree 20-year old bachelor whose lifestyle is supported by expected payments from a trust fund established by a relative who has since passed away. The trust fund will pay you $x when you turn 21 (a year from now), another $y when you turn 25 and $z when you turn 30. You plan to marry a rich heiress on your 30th birthday and therefore only have to support yourself for the next 10 years. The bank that maintains the trust account is willing to lend money to you at a 10% interest rate and pays 10% interest on savings. (Assume annual compounding.)
A: Suppose x = y = z = 100,000.
(a) What is the most that you could consume this year?
(b) What is the most you could spend at your bachelor party 10 years from now if you find a way to live without eating?
B: Define your 10 year inter temporal budget constraint mathematically in terms of x, y and z, letting c1 denote this year’s consumption, c2 next year’s consumption, etc. Let the annual interest rate be denoted by r .