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# Analyzing the Time Value of Money

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Sally and Ed have approached you with their financial problems, described below.

Situation #1

Sally and Ed have \$10,000 cash to invest with a bank offering a 4% interest rate. They are not sure whether to invest the cash with the interest compounded quarterly, semi-annually, or annually. Calculate the balance at the end of 5 years generated by investing \$10,000 at 4% in an interest bearing account that is compounded quarterly, semi-annually, or annually.

Situation #2

Shangri-la Summers, one of BC's biggest customers, has requested a loan with favorable terms. Sally and Ed decide to offer this customer a \$40,000 five-year note receivable. You recommend that since this is your best customer, they offer a 4% interest rate rather than the 7% going rate.

Situation #3

Sally would like to retire in 15 years. She estimates that her life expectancy upon retirement would be 17 years and she would require \$60,000 a year to live comfortably. Use a discount rate of 5%.

Situation #4

BC Corporation has a balloon payment coming due from a recent acquisition. They need to have \$150,000 set aside 5 years from now. They can either make payments into the fund at the beginning of the year or at the end of the year. The current discount rate is 6%.

Situation #5

Ed won the lottery! He can either take the \$5,000,000 prize now or receive the payments over the next 20 years.

Using your knowledge of the time value of money, offer them guidance in each situation. Include the following in your answer:
- What TVM concept(s) is represented in the situation?
- What is the value of the money represented by the situation?
- How did you arrive at the value?

#### Solution Preview

Situation #1
TVM concept represented: Future value of a single amount with compounding interest

Quarterly
Value: \$12,202
Explanation:
Interest = 4%/4 = 1%
Period: 5 years x 4 quarters = 20 period
Future value = \$10,000*(1+1%)^20 = \$12,202

Semi-annual
Value: \$12,190
Explanation:
Interest = 4%/2 = 2%
Period: 5 years x 2 semi-annual = 10 period
Future value = \$10,000*(1+2%)^10 = \$12,190

Annual
Value: \$12,167
Explanation:
Interest = 4%
Period: 5 years
Future value = \$10,000*(1+4%)^5 = \$12,167

Situation #2
TVM concept ...

#### Solution Summary

The solution goes into a great amount of detail analyzing the five above scenarios. The concepts related to the time value of money are all very well explained and easy to understand. The solution can be followed very easily by anyone who has some understanding of the concepts beforehand. In total the solution is 345 words in length.

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