Time value of money scenarios

Time Value of Money, Opportunity Cost, and Income Taxes Worksheet

FP/100 Version 1

1

University of Phoenix Material

Time Value of Money, Opportunity Cost, and Income Taxes Worksheet
Scenario 1: Time Value of Money / Cash Management Products

1. Use this Bankrate’s Simple Savings calculator to complete Scenario 1: http://www.bankrate.com/calculators/savings/simple-savings-calculator.aspx. You will enter the Initial Amount of Savings (Present Value), Annual Interest Rate (Rate of Return), and Number of Periods/Years into the calculator. The calculator will compute the Future Values.

In this scenario you will look at the impact of interest rates on your savings. Suppose that you have $2,000 of savings. You don’t anticipate needing to dip into these funds in the next five years. Based on the information provided in the table, calculate the future value (FV) of $2,000 at the end of years 1 and 5 if it were to be completely invested in each of the different cash management products.

Enter your answers in the indicated cells of the table below. The Restrictions/Fees on Product Usage column relates to question 2 of Scenario 1.

Product

Annual Interest Rate

Restrictions/Fees on Product Usage

FV at end of Year 1

FV at end of Year 5

Checking Account

0.00%

· No minimum

· No limit on withdrawals

Answer: $2,000

Calculator Inputs:

Initial Amount: $2,000

Annual Interest Rate (compounded quarterly): 0.00%

Number of Years: 1

Answer: $2,000

Calculator Inputs:

Initial Amount: $2,000

Annual Interest Rate (compounded quarterly): 0.00%

Number of Years: 5

Savings Account

1.50%

· No minimum

· Limited to 3 withdrawals per month

Answer: $2,030.17

Calculator Inputs:

Initial Amount: $2,000

Annual Interest Rate (compounded quarterly): 1.50%

Number of Years: 1

Answer: $2,155.47

Calculator Inputs:

Initial Amount: $2,000

Annual Interest Rate (compounded quarterly): 1.50%

Number of Years: 5

Certificate of Deposit (CD)

5%

· $500 minimum balance

· Early withdrawal penalty: 180 days of interest plus $25

Answer: $2,101.89

Calculator Inputs:

Initial Amount: $2,000

Annual Interest Rate (compounded quarterly): 5%

Number of Years: 1

Answer: $2,564.07

Calculator Inputs:

Initial Amount: $2,000

Annual Interest Rate (compounded quarterly):

5%

Number of Years: 5

2. Based on your calculations and on all you have learned this week, how would you choose to save your $2,000? Consider things such as rate of return, inflation, taxes, liquidity, safety, restrictions, and fees, and explain the rationale for your decision. Respond in at least 50 words.

Scenario 2: Time Value of Money / Compounding Interest

3. Use this Bankrate’s Simple Savings calculator to complete Scenario 2: http://www.bankrate.com/calculators/savings/simple-savings-calculator.aspx. You will enter the Initial Amount of Savings (Present Value), Annual Interest Rate (Rate of Return), Interest Compounded, and Number of Periods/Years into the calculator. The calculator will compute the Future Values.

In this scenario you will start with a big deposit and see how interest, compounding, and time will change the balance over time. Suppose that you inherit $10,000 from your late uncle. You save this money and do not deposit any more money to the account. Determine how much money you would have at the end of each of the periods for each of the scenarios in the table below, assuming that you don’t make any withdrawals from the account over the period.

Enter your answers in the indicated cells of the table below:

Annual Interest Rate

Interest Compounded

FV at the end of Year 5

FV at the end of Year 10

FV at the end of Year 30

2.00%

Annually

Answer: $11,040.81

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 2.00%

Compounded: Annually

Number of Years: 5

Answer: $12,189.94

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 2.00%

Compounded: Annually

Number of Years: 10

Answer: $18,113.62

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 2.00%

Compounded: Annually

Number of Years:

2.00%

Quarterly

Answer: $11,048.96

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 2.00%

Compounded:Quarterly

Number of Years: 5

Answer: $12,207.94

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 2.00%

Compounded: Quarterly

Number of Years: 10

Answer: $18,193.97

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 2.00%

Compounded:Quarterly

Number of Years: 30

8.00%

Annually

Answer: $14,693.28

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 8.00%

Compounded: Annually

Number of Years: 5

Answer: $21,589.25

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 8.00%

Compounded: Annually

Number of Years: 10

Answer: $100,626.57

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 8.00%

Compounded: Annually

Number of Years: 30

8.00%

Quarterly

Answer: $14,859.47

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 8.00%

Compounded:Quarterly

Number of Years: 5

Answer: $22,080.40

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 8.00%

Compounded: Quarterly

Number of Years: 10

Answer: $107,651.63

Enter your inputs:

Initial Amount: $10,000

Annual Interest Rate: 8.00%

Compounded: Quarterly

Number of Years: 30

4. Based on your calculations above, explain in your own words the impact of compounding interest.

Scenario 3: Cost of Credit / Opportunity Cost / Trade-Offs

5. In this scenario you will calculate the monthly payment and total interest paid on a car loan. Suppose that you need $15,000 to buy a used vehicle to get back and forth to work and school. You have $7,500 in a money market fund earning 1.00% per year, but you are not sure you want to use any or all of that money.

Using the tables in Exhibit 1-D, located on pp. 42-43 in the Ch. 1 Appendix of Focus on Personal Finance, determine the total amount of payment due at the end of each year, and divide by 12 to estimate the monthly payment for each of the following loan scenarios. Also, calculate the total amount of interest you would pay over the life of each loan. Be sure to show your work for opportunities to earn partial credit, where applicable.

For example, if you have the correct formula but put a decimal in the wrong spot you could earn partial credit. The first row in the table has been completed to demonstrate you how work can be shown.

Loan Amount

Interest Rate

Term

Monthly Loan Payment = Amount Borrowed divided by “Table Factor in Exhibit 1-D” divided by 12

Total Amount of Interest = (Monthly Loan Payment * Term * 12) - Loan Amount

$7,500

6%

3 years

Example:

7500/2.673=2,805.84

2,805.84/12= 233.82

Example:

(233.82*3*12) - 7,500= 917.52

$7,500

6%

5 years

7,500/4.329=1,732.50

1,732.50/12=144.38

(144.38*5*12)=8,662.80

8,662.80-7,500=1,162.80

$10,000

6%

5 years

10,000/4.329=2,310.00

2,310.00/12=192.50

(192.50*5*12)=11,550.00

11,550.00-10,000=1,550.00

$15,000

6%

5 years

15,000/4.329=3,465.00

3,465.00/12=288.75

(288.75*5*12)=17,325.00

17,325.00-15,000=2325.00

6. Based on the above calculations, the price of the car, and the money available in a money market fund, which loan option would you suggest to someone purchasing a vehicle? Please explain the rationale and considerations for your decision.

I would recommend the third loan, $10,000 at 6% over 5 years and use $5000 from the money they have in the money market fund. The person in this example is in school and probably has other expenses so the payment would be low and they would have $2500 left for other expenses from their money market fund. In the end they would pay a little more in interest than the first and second loan but not much more. Ideally, if their personal finances would allow it, loan number one would be great because they would not pay much interest at all but the monthly payment would be much higher than the others.

7. In your own words, how would you summarize “opportunity cost”? How does the concept of opportunity cost apply to this decision? Explain in a brief paragraph.

Opportunity cost is basically weighing out all your options and choosing the best choice at that particular time. The gain lost from making this choice over another option is “opportunity cost”. It could be a gamble in some instance but one must take all factors into consideration. It applies in this decision because the person must choose to either continue saving the $7500 they have invested or use it towards the purchase of a new car. Taking out a loan would let him keep part or all of the money he has invested or he could use it all and pay a smaller loan off faster. It’s a personal decision that one must make with information gathered beforehand.

Income Taxes

Each year you will need to file a federal income tax return by April 15th. While you may use software or a tax preparation professional to help you complete your return, there are still some terms of which you should have a basic understanding. Respond to the following to demonstrate your understanding. Each response should be at least 50 words. 

8. Explain the differences between taxable income and adjusted gross income.

9. In your own words, define tax deduction, exemption, and tax credit.