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# Investments and Compound Interest

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A grandmother is looking for a plan to finance her new grandchild's college education. She has \$62,000 to invest. Search the internet and locate a long-range investment plan, CD, Savings Bond, etc, for the grandmother. The plan is to earn compound interest.

Calculate the future value of the investment. You must use the advertised interest rate, the number of compounding periods per year, and the time the funds will be invested. If you are not given the number of compounding periods a year, make it up.

The principal is \$62,000. This is P.
Research the annual interest rate for your investment. This is r.
State the time in years for the investment (as in when the new grandchild will be attending college). This is t.
State the number of compounding periods per year. This is n.
Model the future value of Grandma's investment as an exponential function, with time as the independent variable: F(t) = P(1 + r/n) nt
State the future value of Grandma's investment.
Use the internet or library resources to find the average cost of a college education today; will grandma's investment be able to cover the cost in today's dollars; what about in the future?
Summarize your findings in writing using proper style and grammar.
Include references formatted according to APA style.

#### Solution Preview

Step 1: Search the internet and locate a long-range investment plan, CD, ...

Solution: Go to www.bankrate.com. This site lists the interest rates for different banks based on the type of investment.
Found a bank you like and use their rate. This will be r. Note r should be written as a decimal.
For example: If Bank A has an interest rate of 2.98% for its CDs, then r = 0.0298. (2.98/100 = 0.0298)

Step 2: Model and calculate the future value of the investment.

Solution: This is a compound interest plan so F(t) = P(1+r/n)^nt.

P = 62,000
r = 0.0298 (number from Step 1)
t = 18 ...

#### Solution Summary

Steps for creating a compound interest function and direction to completing an internet search for interest rate.

\$2.19

Individual Work 1

Please respond to all of the following prompts in the class discussion section of your online course:
1. You have been asked by your friend to describe this topic. Your friend knows very little about math, but learns well with pictures and analogies. Come up with a creative way to explain the concept of "compound interest" to your friend.
2. Go to http://bankrate.com/brm/calc/savecalc.asp. If you want to save \$25,000 for a down payment on a house and you have ten years to save this amount, how much would you need to save monthly to achieve this goal if the interest rate is 5% compounded monthly. What happens if you can increase your interest rate to 8%? NOTE: Enter \$100 for the "How much money can you spare for your first deposit or investment".
3. Develop a personal example of compound interest that differs from the example in question 2.

Individual Work 2
Scenario: A client comes to you for investment advice on his \$500,000 winnings from the lottery. He has been offered the following options by three different financial institutions and requests assistance to help understand which option would be the best for his investment.
- Option 1: 6% compounded interest quarterly for 5 years.
- Option 2: 8% compounded interest annually for 5 years.
Write a professional memo that covers the following information:
a. Explain to the client the main differences between simple interest versus compound interest.
b. Explain the results of the three different options by showing the client the step-by-step calculations.
c. Explain which investment option is better for your client and why.
The total minimum document length should be one page.

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