Assume that 4 years from now you will need $1,000. Your bank compounds interest

Question

Assume that 4 years from now you will need $1,000. Your bank compounds interest at an 8% annual rate.

a. How much must you deposit 1 year from now to have a balance of $1,000 4 years from now?

b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, how much each of the 4 payments be?

c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 1 year from now, which would you choose?

d. If you have only $750 1 year from now, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 4 years from now? 7.4%

e. Suppose you can deposit only $186.29 each at Years 1 through 4, but you still need $1,000 at Year 4. What interest rate, with annual compounding, must you seek out to achieve your goal?

Explanation / Answer

Let the four year considered be 2003,2004,2005,2006
Now year 2002

a. Future Value = 1000 = Investment * (1.08)^3

Investment = $793.83

b. Future Value = $1000= Annual Amount * (PV value 2003 + PV value 2004 + PV value 2005 + PV value 2006)

Value = $1000 = Annual Amount * (1.259712 + 1.1664 + 1.08 + 1.0)

Value = $1000 = Annual Amount * (4.506112)

Annual amount = $221.92

c. Future Value = 750 * (1.08)^3 = $944.78

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