BUS3062 Fundamentals of Finance |
Time Value of Money (TVM) – Analyzing Single Cash Flows |
Practice Problem Worksheet Using Excel Formulas |
Make sure to read and study Chapter 4, "Time Value of Money 1: Analyzing Single Cash Flows," from your M: Finance text before reviewing the following problems and solutions. |
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Be advised that annual compounding is used in each of these practice problems, unless more frequent compounding is otherwise specifically disclosed. |
Future Value |
Future Value Problem 1) Here is a simple future value problem: |
How much would you have in your savings account after 5 years if you deposited $1,000 today and it earned 6% interest per year? The correct answer is $1,338.23 determined below. |
Solution: First, identify this is a future value problem (this is determined because we are asked how much money we will have (in the future.) That is our clue that this is a FV problem. |
Next identify the known variables: |
The interest rate: I = 6% (or 0.06 expressed as a decimal) |
The number of time periods: N = 5 |
The present value: PV = 1,000 (note that you will enter PV as a negative number below) |
Next using the Excel, Formulas, Financial, FV formula that reads as follows: |
FV = (Int rate, Number of periods, next enter 0 because there are no recurring payments for this type of problem, enter the Present Value as a negative number) |
inputting the numbers into the Excel FV formula in the exact order prescribed by the formula (click on Cell B32 to see the contents of the cell as inputted): |
FV = |
$1,338.23 |
Future Value Problem 2 |
How much would you have after 10 years if you deposited $1,500 today and it earned 5% interest per year? The correct answer is $2,443.34 determined below. |
FV = |
$2,443.34 |
Present Value |
Present Value Problem 1 |
How much would you need to deposit today if you wanted to end up with $10,000 in your savings account in 8 years and the deposit would earned 7% interest per year? The correct answer is $5,820.09 determined below. |
Solution: First, identify this is a present value problem (this is determined because we are asked how much money we need to deposit (today.) That is our clue that this is a PV problem. |
Next identify the known variables: |
The interest rate: I = 7% (or 0.07 expressed as a decimal) |
The number of time periods in years: N =8 |
The future value: FV = 10,000 |
Next using the Excel, Formulas, Financial, PV formula that reads as follows: |
PV = (Int rate, Number of periods, next enter 0 because there are no recurring payments for this type of problem, enter the Future Value) |
Inputting the numbers into the Excel PV formula in the exact order prescribed by the formula (click on Cell B68 to see the contents of the cell as inputted): |
PV = |
($5,820.09) |
(Note that PV is solved showing it as a negative number. This is because of the formula that is used to solve the equation and represents that $5,820.09 must be paid out (an outflow) in order to receive the 10,000 (inflow) amount in the future. Even though the Excel mathematical equation solves the PV as a negative number, one should simply refer to the PV as $5,820.09 without reference to it as a negative number.) |
Present Value Problem 2 |
What is the present value of $15,000 payment planned to be made in 12 years when the discount rate is 7%? The correct answer is $6, 660.18 determined below. |
PV = |
($6,660.18) |
Time Period |
Solving for Time: |
Problem 1: Here is a simple time value of money problem solving for number of periods: |
How long would it take a deposit of $2,500 to grow to $3,500 assuming it earned 4.5% annual interest? The correct answer is 7.64 years determined below. |
Solution: First, identify this is a time value of money problem attempting to solve for time. (Such time period problems are usually easy to identify and often state "how long will it take.") |
Next identify the known variables: |
The interest rate: I = 4.5% (or 0.045 expressed as a decimal) |
The present value: PV = 2,500 (note you will enter PV as a negative number below) |
The future value: FV = 3,500 |
Next using the Excel, Formulas, Financial, NPER formula that reads as follows: |
NPER = (Int rate, next enter 0 because there are no recurring payments for this type of problem, enter the Present Value amount as a negative number, enter the future value amount) |
inputting the numbers into the Excel NPER formula in the exact order prescribed by the formula (click on Cell B109 to see the contents of the cell as inputted): |
NPER = |
7.64 |
years |
Problem 2 |
How long would it take a deposit of $150 to grow to $300 (another way of saying this would be "how long would it take any deposit to double") assuming it earned 7.5% annual interest? The correct answer is 9.58 years determined below. |
NPER = |
9.58 |
years |
Annual Rate of Return |
Solving for Interest Rate |
Problem 1: Here is a simple problem solving for interest rate (annual rate of return): |
What interest rate must you earn to turn your $3,000 deposit into $4,000 within 6 years? The correct answer is 4.91% determined below. |
Solution: First, identify this is a time value of money problem attempting to solve for a requested interest rate. Such interest rate problems often state "what rate of interest must be earned…" or similar wording. |
Next identify the known variables: |
The number of time periods in years: N = 6 |
The present value: PV = 3,000 (note that you will enter PV as a negative number below) |
The future value: FV = 4,000 |
Next using the Excel, Formulas, Financial, RATE formula that reads as follows: |
RATE = (Number of time periods, next enter 0 since there are no recurring payments for this problem, enter the Present Value amount as a negative number, enter the Future Value amt.) |
inputting the numbers into the Excel RATE formula in the exact order prescribed by the formula (click on Cell B148 to see the contents of the cell as inputted): |
RATE = |
4.91% |
(Make sure you change the number of decimals in the formula cell so you show at least 4 decimal places as is shown to the left, otherwise, your response would show 5% and that is not sufficiently exact and would be marked as incorrect.) |
RATE 2) Here is a simple time value of money solving for interest rate practice problem: |
If you had $10,000 and needed it to grow to $12,000 within 3 years, what annual rate of return would you need to receive? The correct answer is 6.27% determined below. |
NPER = |
6.27% |
(Make sure you change the number of decimals in the formula cell so you show at least 4 decimal places as is shown to the left, otherwise, your response would show 6% and that is not sufficiently exact and would be marked as incorrect.) |
Differing Interest Rates |
Solving for Future Value with differing rates of interest: |
Problem 1: Here is a simple FV problem solving with differing interest rates: |
A $1,500 deposit you make today is expected to earn 3% the first year, 4% the second year, 4.5% the third year, and 5% the fourth year. How much would you have at the end of the fourth year? The correct answer is 1,763.06 determined below. |
Solution: First, identify this is a future value problem with differing rates of interest. |
Next, the answer is calculated by taking the original deposit and multiplying it by (1+ Interest Rate) for each annual period's interest rate, algebraically shown as follows: ($1,500 original deposit x 1.03 x 1.04 x 1.045 x 1.05 = $1,763.06 (also click on Cell B181 to see the contents of the cell as solved algebraically without the use of an Excel Formula function): |
Answer = |
$ 1,763.06 |
Problem 2 |
A deposit of $850 earns the following interest rates: 5% the first year, 5.5% the second year, and 6% the third year. What would be third year future value? The correct answer is $998.08 determined below. |
Answer = |
$ 998.08 |
Compounding Frequency |
Compounding Frequency: |
Each of the above problems assumes interest is compounded on an annual basis. However, in actuality, many financial obligations are compounded more frequently, such as bond interest (normally semi-annual frequency as we will see in Week 3), many bank CDs (quarterly, or more frequent compounding), home mortgage and car financing (monthly frequency.) Review the section, "Compounding Frequency," in Chapter 5 of your M: Finance text for a further discussion of this topic. |