Exam 9: The Time Value of Money

Sara Shouppe has invested $100,000 in an account at her local bank. The bank will pay her a constant amount each year for 6 years, starting one year from today, and the account's balance will be 0 at the end of the sixth year. If the bank has promised Ms. Shouppe a 10% return, how much will they have to pay him each year?

To save for her newborn son's college education, Lea Wilson will invest $1,000 at the beginning of each year for the next 18 years. The interest rate is 12 percent. What is the future value?

Ian would like to save $2,000,000 by the time he retires in 40 years. If he believes that he can achieve a 7% rate of return, how much does he need to deposit each year to achieve his goal?

Kimberly Ford invested $10,000 10 years ago at 16 percent, compounded quarterly. How much has she accumulated?

The interest factor for the future value of an annuity is simply the sum of the interest factors for the future value using the same number of periods.

Marcia Stubern is planning for her golden years. She will retire in 20 years, at which time she plans to begin withdrawing $60,000 annually. She is expected to live for 20 years following her retirement. Her financial advisor thinks she can earn 9% annually. How much does she need to invest each year to prepare for her financial needs after her retirement?

The interest factor for the present value of a single sum is equal to (1 + i)/i.

An amount of money to be received in the future is worth less today than the stated amount.

The future value of an annuity table provides a short-cut for calculating the future value of a steady stream of payments, denoted as A. The same value can be calculated directly from the following equation:

Mr. Blochirt is creating a college investment fund for his daughter. He will put in $1,000 per year for the next 15 years and expects to earn a 6% annual rate of return. How much money will his daughter have when she starts college?

If an individual's cost of capital were 6%, he/she would prefer to receive $110 at the end of one year rather than $100 right now. (App. B: 6%, 1 period) = $110 x .0.943 = $104

Samuel Johnson invested in gold U.S. coins ten years ago, paying $216.53 for one-ounce gold "double eagle" coins. He could sell these coins for $734 today. What was his annual rate of return for this investment?

Mike Carlson will receive $12,000 a year from the end of the third year to the end of the 12thyear (10 payments). The discount rate is 10%. The present value today of this deferred annuity is:

Cash flow decisions that ignore the time value of money will probably not be as accurate as those decisions that do rely on the time value of money.

Dan would like to save $1,500,000 by the time he retires in 25 years and believes he can earn an annual return of 8%. How much does he need to invest in each of the following years to achieve his goal?

The time value of money concept is fundamental to the analysis of cash inflow and outflow decisions covering periods of over one year.

Sydney saved $10,000 during her first year of work after college and plans to invest it for her retirement in 40 years. How much will she have available for retirement if she can make 8% on her investment?

Ambrin Corp. expects to receive $2,000 per year for 10 years and $3,500 per year for the next 10 years. What is the present value of this 20 year cash flow? Use an 11% discount rate.

In determining the interest factor (IF) for the present value of $1, one could use the reciprocal of the IF for the future value of $1 at the same rate and time period.

The present value of an annuity table provides a short-cut for calculating the future value of a steady stream of payments, denoted as A. The same value can be calculated directly from the following equation: