Chapter 5 The Time Value of Money

74) In order to send your first child to Law School when the time comes, you want to accumulate $40,000 at the end of 18 years. Assuming that your savings account will pay 6% compounded annually, how much would you have to deposit if:

a. You want to deposit an equal amount at the end of each year?

b. You want to deposit one large lump sum today?

75) Cindy wants $2.5 million for her retirement at age 65. Cindy is 25 years old today and plans to deposit equal amounts each year starting on her 26th birthday and ending on her 65th birthday. If her investments earn 6% per year, how much must each deposit be?

76) A retirement home in Florida costs $200,000 today. Housing prices in Florida are increasing at a rate of 4% per year. Joe wants to buy the home in 8 years when he retires. Joe has $25,000 right now in a savings account paying 8% interest per year. Joe wants to make eight equal annual deposits into the savings account starting today. How much must each deposit be so Joe will have enough money in his savings account to buy the retirement home when he retires?

Learning Objective 3

1) A return of 12% compounded annually is the same as a return of 1% per month.

2) The price of a computer today is $400 and inflation is 5% per year. Therefore, in two years the price of the computer is expected to be $440.

3) If we invest money for 10 years at 8 percent interest, compounded semiannually, we are really investing money for 20 six-month periods, and receiving 4 percent interest each period.

4) For a given stated interest rate, an investor would receive a greater future value with daily compounding as opposed to monthly compounding.

5) A certificate of deposit that pays 9.8% compounded monthly is better than a similar certificate of deposit that pays 10% compounded only once per year.

6) A compound annuity involves depositing or investing a single sum of money and allowing it to compound for a certain number of years.

7) Tim invested $1,000 in a mutual fund paying 8% per year. John invested $500 in the same fund. If both Tim and John keep their money invested for the same period of time, Tim will end up with twice as much money as John.