Exam 9: The Time Value of Money

Dr. Stein has just invested $10,000 for his son (age 7). The money will be used for his son's education 10 years from now. He calculates that he will need $21,598 for his son's education by the time the boy goes to school. What rate of return will Dr. Stein need to achieve this goal? Choose the closest answer.

How much must you invest today at 8% interest in order to see your investment grow to $8,000 in 10 years?

Mr. Fish wants to build a house in ten years. He estimates that the total cost will be $150,000. If he can put aside $10,000 at the end of each year, what rate of return must he earn in order to have the amount needed?

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

If a single amount were put on deposit at a given interest rate and allowed to grow, its future value could be determined by reference to a "future value of $1" table.

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

If Gerry makes a deposit of $1,500 at the end of each quarter for five years, how much will he have at the end of the five years assuming a 12% annual return and quarterly compounding?

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

Ian would like to save $2,000,000 by the time he retires in 30 years. If he believes that he can achieve a 6% rate of return, how much does he need to deposit each year, starting one year from now, to achieve his goal?

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

The formula PV = FV(1 + n)ⁱ will determine the present value of $1.

Babe Ruth Jr. has agreed to play for the Cleveland Indians for $3 million per year for the next 10 years. What table would you use to calculate the value of this contract in today's dollars?

The future value of an annuity table provides a "shortcut" 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: $\mathrm { FV } _ { \mathrm { A } } = \mathrm { A } \left[ \frac { 1 } { ( 1 + i ) } \right] ^ { 1 } + \mathrm { A } \left[ \frac { 1 } { ( 1 + i ) } \right] ^ { 2 } + \ldots \mathrm { A } \left[ \frac { 1 } { ( 1 + i ) } \right] ^ { n }$

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

The present value of an annuity table provides a "shortcut" for calculating the present value of a steady stream of payments, denoted as A. The same value can be calculated directly from the following equation: $\mathrm { PV } _ { \mathrm { A } } = \mathrm { A } \left[ \frac { 1 } { ( 1 + i ) } \right] ^ { 1 } + \mathrm { A } \left[ \frac { 1 } { ( 1 + i ) } \right] ^ { 2 } + \ldots \mathrm { A } \left[ \frac { 1 } { ( 1 + i ) } \right] ^ { n }$

To determine the current worth of four annual payments of $1,000 at 4% annual interest, one would refer to a time value of money table for the present value of $1.

The amount of annual payments necessary to accumulate a desired future total can be found by reference to the present value of an annuity table.

Football player Walter Johnson signs a contract calling for payments of $250,000 per year, which begins 10 years from now and then continue for five more years after that. To find the value of this contract today, which table or tables should you use?

The concept of present value is a sum payable in the present is worth less in the future than in the stated amount today.

The future value of an ordinary annuity assumes that the payments are received at the end of the year and that the last payment does not compound.