# How Does Money Grow Over Time?

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2 Activity Sheet 1: Saving for Retirement Help Bob and Sidney calculate the potential gains for the three different s by completing the amounts in the grayed section of the table. Results are rounded to the whole dollar amount. Compound interest is the amount of investment + earned interest x the interest rate = the interest earned: Scenario One Scenario Two Scenario Three Age Savings interest rate Savings Certificate of deposit interest rate* Certificate of deposit IRA Rate of Return IRA 22 2% 4% 5% 23 2% 4% 5% 24 2% 4% 5% 25 2% 4% 5% 26 2% 4% 5% 27 2% \$1,126 6% \$1,290 5% \$1, % \$1,171 6% \$1,367 9% \$1, % \$1,195 6% \$1,449 4% \$1, % \$1,219 6% \$1,536 4% \$1, % 6% 4% 32 3% \$1,293 8% \$1,758 4% \$1, % \$1,357 8% \$1,899 11% \$1, % \$1,425 8% \$2,051 11% \$2, % \$1,497 8% \$2,215 10% \$2, % 8% 10% 37 5% \$1,650 8% \$2,584 10% \$2, % \$1,732 8% 9% \$3, % \$1,802 8% 9% 40 4% \$1,874 8% \$3,255 7% \$3, % 8% 7% 42 3% \$1,988 8% \$3,796 7% \$4, % \$2,067 8% \$4,100 9% \$4, % \$2,171 8% 11% \$4, % \$2,323 8% 11% \$5, % 8% 11% 47 7% \$2,659 10% \$5,681 11% \$6, % \$2,845 10% \$6,249 9% \$7, % \$2,988 10% \$6,874 9% \$8, % \$3,137 10% \$7,562 7% \$8, % 10% 7% 52 3% \$3,393 6% \$8,817 5% \$9, % 6% 5% \$10, % 6% \$9,907 5% 55 3% \$3,707 6% \$10,501 5% \$11, % 6% 5% 57 3% \$3,933 4% \$11,577 4% \$12, % \$4,051 4% \$12,040 5% \$12, % \$4,173 4% \$12,521 6% \$13, % \$4,298 4% \$13,022 6% \$14, % 4% 6% 62 4% 5% 6% 1 of 2

3 * 5 year CD 1. Based on the results above, which savings vehicle yields the best results for retirement? Why? 2. Assume the interest rate for the savings remained at 2%, the interest rate for the CD remained at 4%, and the interest rate of the IRA remained at 5%. Using the Rule of 72, how many years would it take for each savings type to double? 3. Using the assumption stated above about interest rates for the savings types above, how much more would Bob and Sidney have earned at the age of 22, if they had invested their respective \$1,000 at the age of 18? To answer, first calculate how much they would have earned from the ages of 18 to 22. Then subtract that amount from \$ The story of Bob and Sidney includes changes in interest rates throughout the years. Which type of savings is the most stable? Which the most volatile? 5. The Certificate of Deposit maintains the same interest rate over the deposit period. What is a possible disadvantage to this kind of savings? When would you advise the young men to consider it most useful? 6. The Individual Retirement Account seems to have risks and rewards. Based upon the chart, is the IRA a sound investment over the 40 years? What could happen to have you change your advice? 2 of 2

4 Activity Sheet 1: Answer Key Help Bob and Sidney calculate the potential gains for the three different s by completing the amounts in the grayed section of the table. Results are rounded to the whole dollar amount. Compound interest is the amount of investment + earned interest x the interest rate = the interest earned: Age Scenario One Scenario Two Scenario Three Savings interest rate Savings Certificate of deposit interest rate* Certificate of deposit IRA Rate of Return IRA 22 2% \$1,020 4% \$1,040 5% \$1, % \$1,040 4% \$1,081 5% \$1, % \$1,061 4% \$1,125 5% \$1, % \$1,082 4% \$1,170 5% \$1, % \$1,104 4% \$1,217 5% \$1, % \$1,126 6% \$1,290 5% \$1, % \$1,171 6% \$1,367 9% \$1, % \$1,195 6% \$1,449 4% \$1, % \$1,219 6% \$1,536 4% \$1, % \$1,256 6% \$1,628 4% \$1, % \$1,293 8% \$1,758 4% \$1, % \$1,357 8% \$1,899 11% \$1, % \$1,425 8% \$2,051 11% \$2, % \$1,497 8% \$2,215 10% \$2, % \$1,572 8% \$2,392 10% \$2, % \$1,650 8% \$2,584 10% \$2, % \$1,732 8% \$2,790 9% \$3, % \$1,802 8% \$3,013 9% \$3, % \$1,874 8% \$3,255 7% \$3, % \$1,930 8% \$3,515 7% \$3, % \$1,988 8% \$3,796 7% \$4, % \$2,067 8% \$4,100 9% \$4, % \$2,171 8% \$4,428 11% \$4, % \$2,323 8% \$4,782 11% \$5, % \$2,486 8% \$5,165 11% \$6, % \$2,659 10% \$5,681 11% \$6, % \$2,845 10% \$6,249 9% \$7, % \$2,988 10% \$6,874 9% \$8, % \$3,137 10% \$7,562 7% \$8, % \$3,294 10% \$8,318 7% \$9, % \$3,393 6% \$8,817 5% \$9, % \$3,495 6% \$9,346 5% \$10, % \$3,600 6% \$9,907 5% \$10, % \$3,707 6% \$10,501 5% \$11, % \$3,818 6% \$11,131 5% \$11, % \$3,933 4% \$11,577 4% \$12, % \$4,051 4% \$12,040 5% \$12, % \$4,173 4% \$12,521 6% \$13, % \$4,298 4% \$13,022 6% \$14,376 1 of 3

5 61 3% \$4,427 4% \$13,543 6% \$15, % \$4,604 5% \$14,220 6% \$16,153 * 5 year CD 1. Based on the results above, which savings vehicle yields the best results for retirement? Why? The best results would have to be the IRA, Scenario 3 because from the ages of 22-62, its is the highest. 2. Assume the interest rate for the savings remained at 2%, the interest rate for the CD remained at 4%, and the interest rate of the IRA remained at 5%. Using the Rule of 72, how many years would it take for each savings type to double? Savings Account - 2% = 36 years CD - 4% = 18 years IRA - 5% = 14.4 years 3. Using the assumption stated above about interest rates for the savings types above, how much more would Bob and Sidney have earned at the age of 22, if they had invested their respective \$1,000 at the age of 18? To answer, first calculate how much they would have earned from the ages of 18 to 22. Then subtract that amount from \$1000. Savings Account = 104 CD = 217 IRA = The story of Bob and Sidney includes changes in interest rates throughout the years. Which type of savings is the most stable? Which the most volatile? CD is the most stable because its interest rates do not change over the deposit period. The interest rates don t differ much. On the other hand, the IRA interest rates are unstable. They usually change every couple of years with very major interest rate differences. 5. The Certificate of Deposit maintains the same interest rate over the deposit period. What is a possible disadvantage to this kind of savings? When would you advise the young men to consider it most useful? You want your investment to grow, but if the CD maintains a low rate for 5 years, you might of just wasted valuable interest. When they grow older and have a larger amount of money in the deposit, it would probably be more beneficial. 6. The Individual Retirement Account seems to have risks and rewards. Based upon the chart, is the IRA a sound investment over the 40 years? What could happen to have you change your advice? The IRA sounds like a really nice investment over 40 years, but if the interest is unstable and decides to drop low for most of the 40 years, then I would change my advice. 2 of 3

7 In an IRA, you can invest in a wide variety of stocks, mutual funds and other investments. Over the last 5 years the average rate of return on the IRA has been 5 % per year. The rate of return for an IRA is not guaranteed. They may earn 5% this year, 10% next year and then lose 5% the year after. A Certificate of Deposit has a guaranteed interest rate, but you cannot use the money for the duration of the CD which can range from six months to more than 10 years. A regular savings has a guaranteed interest rate. The interest rate is much lower than that of the CD, but you can withdraw the money at any time. Ask Which savings plan seems to be the best? Which one will earn each college graduate the most money in 40 years at age 62? Discuss the various answers offered by the students; then take a class vote. Procedure Distribute Activity Sheet 1: Saving for Retirement. Explain that financial planners use a formula to calculate compound interest rates on savings investments, but this formula does not take into interest rate changes that may occur over time. The students can help the two recent graduates by calculating their money based on what they know now. Explain that interest is computed by: the amount of investment + earned interest x the interest rate = the interest earned: For example: Year 1: \$1,000 investment + \$0 x 3% = \$30 (interest) + \$1,000 = \$1,030; Year 2= \$1,030 () x 3% = \$ \$1,030 = \$1, Novice Level Divide the class into SMG teams. Have the students complete the Activity Sheet 1: Saving for Retirement. Demonstrate how to calculate compound interest on a \$1,000 CD invested over 5 years (22 26). Explain how the calculations were made. After completing those calculations, read the table to review the 40-year investment results. Discuss the results. Then read the table on Activity Sheet 1 for scenario two and scenario three. Apprentice Level Have teams complete the calculations for the savings, CD, and IRA over 5 years (22 26). After they complete the calculations, have them read the table to review the 40-year investment results. Discuss the results. 3 of 6

9 Apprentice Level Teacher plays an investment broker; the students are investors. Have the student investors ask investment questions. The types of questions they ask will demonstrate their level of comprehension. (Examples: What is the expected rate of return on my investment? How safe is my investment? Is the investment FDIC insured? How long will I have to leave my investment in the?) Master Level Students are the investment brokers; the teacher is the investor. Ask investment questions of the student brokers. Have them use their charts to demonstrate the best investment options for the teacher. Note: To give sound investment advice the student brokers must determine the teacher s risk tolerance level. Grand Master Level Organized in SMG teams, have students play investment advisors helping a client convert his retirement savings from a bank into an IRA. Their client: Is 25 years old Is financially stable Intends to work for the next 40 years Has saved \$5,460. Using the Internet, newspapers, or other available resources, have students develop a portfolio of three stocks, taking their client s risk tolerance into in their decisions. Have the students calculate the estimated total value of the stocks when their client is ready to retire, based on the stocks performance over the last 5 years and assuming that performance remains steady over the next 40 years. Have the students calculate how much money the client would have if he left his money in the bank until retirement if the bank paid a consistent 4% per year interest rate compounded annually. Have the students calculate how long it would take for the client s money to double in the portfolio vs. in the bank. (Rule of 72) Enrichment Activity Have students prepare personal financial plans that include savings s and stocks. Assume they will contribute \$2,000 per year to these investments for five years. Five years after they make their final contribution, they will use their money to buy a house. Use a 3% yearly interest rate for savings and a 10% yearly return on stocks. Have students use on-line calculators to compute totals. Have students prepare a report explaining how they divided the funds between savings and stocks and what factors influenced their decision including their individual risk tolerances based on what kind of job they think they will have, whether they will have a family and when they will retire. 5 of 6

10 Have them calculate the amount of money they can expect to get from each when they are ready to buy their house. 6 of 6

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