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Exam 13: Time Value of Money

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Question 1

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If you had an investment opportunity that promises to pay you $20,000 in three years and you could earn a 10% annual return investing your money elsewhere,what is the most you should be willing to invest today in this opportunity?

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$15,026.

Question 2

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If you put $200 into a savings account that pays annual compound interest of 8% per year and then withdraw the money two years later,you will earn interest of $32.

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Question 3

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A series of equal periodic payments is referred to as:

What is the value today of receiving $3,000 at the end of each year for the next three years,assuming an interest rate of 3% compounded annually?

How much will $8,000 grow to in five years,assuming an interest rate of 8% compounded quarterly?

Below are excerpts from interest tables for 8% interest. $\begin{array} { l c c c c } & \underline { 1 } & \underline { 2 } & \underline { 3 } & \underline { 4 } \\1 & 1.0000 & 0.92593 & 1.08000 & 0.92593 \\2 & 2.0800 & 0.85734 & 1.16640 & 1.78326 \\3 & 3.2464 & 0.793833 & 1.25971 & 2.57710 \\4 & 4.5061 & 0.73503 & 1.36049 & 3.31213\end{array}$ Column 1 is an interest table for the:

The value today of receiving an amount in the future is referred to as the:

Carol wants to invest money in a 6% CD that compounds semiannually.Carol would like the account to have a balance of $50,000 five years from now.How much must Carol deposit to accomplish her goal?

If you put $500 into a savings account that pays simple interest of 8% per year and then withdraw the money two years later,you will earn interest of $80. Simple interest = ($500  8%)+ ($500  8%)= $80.

Below are excerpts from interest tables for 8% interest. $\begin{array} { c c c c c } & \underline { 1 } & \underline { 2 } & \underline { 3 } & \underline { 4 } \\1 & 1.0000 & 0.92593 & 1.08000 & 0.92593 \\2 & 2.0800 & 0.85734 & 1.16640 & 1.78326 \\3 & 3.2464 & 0.793833 & 1.25971 & 2.57710 \\4 & 4.5061 & 0.73503 & 1.36049 & 3.31213\end{array}$ Column 4 is an interest table for the:

Touche Manufacturing is considering a rearrangement of its manufacturing operations.A consultant estimates that the rearrangement should result in after-tax cash savings of $6,000 the first year,$10,000 for the next two years,and $12,000 for the next two years.Assuming a 12% discount rate,calculate the total present value of the cash flows.

Compute the present value of the following single amounts to be received at the end of the specified period at the given interest rate. $\begin{array} { l c c c } \text { Item } & \begin{array} { c c c } \text { Invested } \\\text { Amount }\end{array} & \begin{array} { c } \text { Interest } \\\text { Rate }\end{array} & \begin{array} { c } \text { Number } \\\text { of } \\\text { Periods }\end{array} \\\hline\text { a. } & \$ 1,500 & 10 \% & 1 \\\text { b. } & \$ 1,500 & 10 \% & 2 \\\text { c. } & \$ 1,500 & 10 \% & 3 \\\text { d. } & \$ 1,500 & 10 \% & 4\end{array}$

Hillsdale is considering two options for comparable computer software.Option A will cost $25,000 plus annual license renewals of $1,000 for three years,which includes technical support.Option B will cost $20,000 with technical support being an add-on charge.The estimated cost of technical support is $4,000 the first year,$3,000 the second year,and $2,000 the third year.Assume the software is purchased and paid for at the beginning of year one,but that technical support is paid for at the end of each year.The discount rate is 8%.Ignore income taxes.Determine which option should be chosen based on present value considerations.

Present value indicates how much a present amount of money will grow to in the future.

How much will $1,000 invested at the end of each year grow to in 20 years,assuming an interest rate of 10% compounded annually?

Today,Thomas deposited $100,000 in a three-year,12% CD that compounds quarterly.What is the maturity value of the CD?

DON Corp.is contemplating the purchase of a machine that will produce net after-tax cash savings of $20,000 per year for 5 years.At the end of five years,the machine can be sold to realize after-tax cash flows of $5,000.Assuming a 12% discount rate,calculate the total present value of the cash savings.

The more frequent the rate of compounding,the more interest that is earned on previous interest,resulting in a higher future value.

If you put $600 into a savings account that pays simple interest of 10% per year and then withdraw the money two years later,you will earn interest of $126.

Which three factors are necessary in calculating the present value of a single amount?