Question

a) You just won $1,000,000 on the lottery. If you chose the payments over 20 years ($50,000 per year) how much is the value of the up-front cash option (present value) if the state uses a 6% rate of return (interest)?

b) Katey needs $10,000 in 4 years to use as a down payment on a house. What amount must she invest today if her investment earns 10%?

c) Linda invested $1500 today in a fund that earns 8% annually. To what amount will the investment grow in 3 years?

d) Tonya, age 22, just started working full-time and plans to deposit $5,000 annually into an IRA earning 8 percent interest compounded annually. How much would she have in 20 years? What if she left it in there until she retires at 62? What if she waits another 10 years before she starts saving? How much will she have when she reaches 62?

Answer 1

Answer a.

Annual payment = $50,000
Number of payments = 20
Interest rate = 6%

Present value = $50,000/1.06 + $50,000/1.06^2 + .... + $50,000/1.06^20
Present value = $50,000 * (1 - (1/1.06)^20) / 0.06
Present value = $573,496

Answer b.

Amount required in 4 years = $10,000
Interest rate = 10%

Present value = $10,000/1.10^4
Present value = $6,830