Question

2. Susan can choose between two different inheritance bundles: Bundle A con- sists of $100 tomorrow and $10 today. Bundle B consists of $30 tomorrow and $60 today. Susan can borrow and lend money at an interest rate of 15%. Consumption goods cost $1 per unit today and there is no inflation. (a) What is the present value of each of the two bundles? What is the future value? (b) Which bundle do you think Susan should choose? Why? (c) Bankers recognize that perfect capital markets make it hard to make money by lending money. Thus they will now pay Susan 15% for any monies that she lends them and they will charge her 50% interest on any monies she borrows. Which bundle will Susan choose? Why?

Answer 1

Answer:

Interest Rate (r) = 15% Concept Used: Future Value (FV-Present Value (PV) * [(1+r) t] Or, PV = FV/[(1+r)^t] Where t- time in years a. Bundle F $100 tomorrow and S10 today Total Present Value of bundle F = 10 + 100/ [(1+15M1/365] 10 + 99.96 109.96 Total Future Value of bundle F PV[(1+)t 109.96 *(115 (1/365)) = 110.002 Bundle P S30 tomorrow and S60 today Total Present Value of bundle P 6030/[(1+15) (1/365)] -89.98 Total Future Value of bundle P PV[1+r)At 89.98 (115 1/365) -90.144

b. Clearly, the nephew should choose bundle F because the present value of bundle F (109.96) is greater than PV of bundle P (89.98) c. For any lending and borrowing rate, it applies to both the bundles, and the present value of bundle F is higher. So whatever the rate may be, the Future value will be higher for Bundle F always. So the nephew should choose bundle F