A dollar left alone in an account that pays compound interest doesn't just sit there, it earns money on the money it already earned. Given enough years, that difference is enormous.
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Interest is what you earn on money you put to work by saving or investing. Savings accounts, IRAs, money market accounts, and CDs all accumulate interest for as long as you hold them, but not all interest works the same way.
A quick way to estimate how long compound interest takes to double your money: divide 72 by the interest rate (drop the % sign). At 3% interest, money doubles in roughly 72 ÷ 3 = 24 years. At 8%, it's 72 ÷ 8 = 9 years.
Same starting balance, same 10% rate, same 20 years, one number apart at the end because of how the interest itself is treated.
Simple interest adds a flat $100 every year, $1,000 × 10% × 20 years, landing at exactly $3,000. Compound interest recalculates 10% against a growing balance each year, $1,000 × (1.10)²⁰, landing at $6,727.50, more than double the simple-interest result. At this higher rate the two lines separate much faster than they would at a lower rate, the gap is already visible within the first several years and keeps accelerating.
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Materials: Activity Sheet 1: Saving for Retirement · online financial calculators such as dinkytown.net or bankrate.com.
Two recent college graduates, talking about saving. Bob wants to open an IRA to save for retirement at 62, forty years away. Sidney thinks a savings account is best, he wants easy access to his money and will worry about retirement once his family is grown.
Financial planners use a formula to calculate compound interest, though it doesn't account for interest rates changing over time the way Bob and Sidney's accounts do below. The rule for one year's growth:
Activity Sheet 1 below leaves a 5-year CD term (ages 22–26, all at 4%) blank for you to compute. The table's own numbers only include a rate starting at age 23; reverse-solving from the given age-27 balance ($1,290 at 6%) shows the CD must also be earning 4% at age 22 itself, consistent with a 5-year CD locking in one rate for its whole term. Applying 4% compound growth for five straight years to a $1,000 principal:
| Age | 22 | 23 | 24 | 25 | 26 |
|---|---|---|---|---|---|
| Balance | $1,040 | $1,082 | $1,125 | $1,170 | $1,217 |
Check: $1,217 × 1.06 (age 27's rate) = $1,290, matching the table's given value exactly.
Complete Activity Sheet 1. Demonstrate how to calculate compound interest on a $1,000 CD invested over 5 years (22–26), using the worked example above as a model. Read the rest of the table to review the 40-year results, then discuss.
Complete the savings, CD, and IRA calculations over the same 5 years (22–26). Read the 40-year results and discuss the factors that affect the rate of return on each account type.
Ask: how does risk tolerance relate to your choice of investment or saving vehicle?
Complete the same calculations, review the 40-year strategy, and discuss the factors driving each account's rate of return. Then discuss the advantages and disadvantages of bank savings versus company stock. Build a list of possible investments that might realistically deliver a 3% growth rate, then do the same for 5%, 6%, and 9%.
Complete the same calculations and discussion as Master Level, then in teams, build a portfolio mixing bank savings and stocks, showing the percentage allocated to each and its expected return. Research real options across print and online sources for consistent returns, then present your portfolio with charts of past and possible future performance.
Help Bob and Sidney calculate the potential gains for three accounts, all starting at $1,000, by filling in the blanks below. Round to the nearest whole dollar. Compound interest: amount of investment + (investment × interest rate) = interest earned, added to the balance.
| Age | Savings Rate | Savings Balance | CD Rate* | CD Balance | IRA Rate | IRA Balance |
|---|---|---|---|---|---|---|
| 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% | $1,340 |
| 28 | 4% | $1,171 | 6% | $1,367 | 9% | $1,461 |
| 29 | 2% | $1,195 | 6% | $1,449 | 4% | $1,519 |
| 30 | 2% | $1,219 | 6% | $1,536 | 4% | $1,580 |
| 31 | 3% | 6% | 4% | |||
| 32 | 3% | $1,293 | 8% | $1,758 | 4% | $1,709 |
| 33 | 5% | $1,357 | 8% | $1,899 | 11% | $1,897 |
| 34 | 5% | $1,425 | 8% | $2,051 | 11% | $2,105 |
| 35 | 5% | $1,497 | 8% | $2,215 | 10% | $2,316 |
| 36 | 5% | 8% | 10% | |||
| 37 | 5% | $1,650 | 8% | $2,584 | 10% | $2,802 |
| 38 | 5% | $1,732 | 8% | 9% | $3,055 | |
| 39 | 4% | $1,802 | 8% | 9% | ||
| 40 | 4% | $1,874 | 8% | $3,255 | 7% | $3,563 |
| 41 | 3% | 8% | 7% | |||
| 42 | 3% | $1,988 | 8% | $3,796 | 7% | $4,079 |
| 43 | 4% | $2,067 | 8% | $4,100 | 9% | $4,446 |
| 44 | 5% | $2,171 | 8% | 11% | $4,935 | |
| 45 | 7% | $2,323 | 8% | 11% | $5,478 | |
| 46 | 7% | 8% | 11% | |||
| 47 | 7% | $2,659 | 10% | $5,681 | 11% | $6,749 |
| 48 | 7% | $2,845 | 10% | $6,249 | 9% | $7,356 |
| 49 | 5% | $2,988 | 10% | $6,874 | 9% | $8,019 |
| 50 | 5% | $3,137 | 10% | $7,562 | 7% | $8,580 |
| 51 | 5% | 10% | 7% | |||
| 52 | 3% | $3,393 | 6% | $8,817 | 5% | $9,639 |
| 53 | 3% | 6% | 5% | $10,121 | ||
| 54 | 3% | 6% | $9,907 | 5% | ||
| 55 | 3% | $3,707 | 6% | $10,501 | 5% | $11,159 |
| 56 | 3% | 6% | 5% | |||
| 57 | 3% | $3,933 | 4% | $11,577 | 4% | $12,185 |
| 58 | 3% | $4,051 | 4% | $12,040 | 5% | $12,795 |
| 59 | 3% | $4,173 | 4% | $12,521 | 6% | $13,562 |
| 60 | 3% | $4,298 | 4% | $13,022 | 6% | $14,376 |
| 61 | 3% | 4% | 6% | |||
| 62 | 4% | 5% | 6% |
* The CD's age-22 rate is not printed in the original worksheet; 4% is used here, matching the 5-year CD term footnote and reverse-solved from the given age-27 balance (see the Worked Example above).
The formula for compound growth: FV = P(1+r)t, where FV is future value, P is the principal, r is the interest rate as a decimal, and t is time in years. Several problems ask you to solve for P instead, dividing FV by (1+r)t.
Rate of return = (this year's price − last year's price) ÷ last year's price. The 2008–2010 rates that follow the housing collapse are unusually low; this range starts a few years earlier to also show a more typical pre-crisis stretch.
| December | Dow Close | Rate of Return | Fed Funds Rate |
|---|---|---|---|
| 2000 | $10,786.85 | — | 6.50% |
| 2001 | $10,021.57 | -7.09% | 1.75% |
| 2002 | $8,341.63 | -16.76% | 1.25% |
| 2003 | $10,453.82 | 25.32% | 1.00% |
| 2004 | $10,783.01 | 3.15% | 2.25% |
| 2005 | $10,717.50 | -0.61% | 4.25% |
| 2006 | $12,463.15 | 16.29% | 5.25% |
| 2007 | $13,264.82 | 6.43% | 4.25% |
| 2008 | $8,776.39 | -33.84% | 0.14% |
| 2009 | $10,428.05 | 18.82% | 0.05% |
| 2010 | $11,577.51 | 11.02% | 0.13% |
The 2000–2007 federal funds figures are approximate year-end target rates; 2008–2010 are effective rates, matching how the original worksheet presented that later stretch.
Becca and David have $11,500 saved for their first child's college fund, ten years away, and plan to add $2,000 every January. Their account compounds annually at 6%. Fill in years 6–10 using: (balance + $2,000 deposit) × 6% = interest; balance + deposit + interest = new balance.
| Year | Value of Investment | After Deposit | Interest | New Amount |
|---|---|---|---|---|
| 0 | $11,500 | $11,500 | $690.00 | $12,190.00 |
| 1 | $12,190.00 | $14,190.00 | $851.40 | $15,041.40 |
| 2 | $15,041.40 | $17,041.40 | $1,022.48 | $18,063.88 |
| 3 | $18,063.88 | $20,063.88 | $1,203.83 | $21,267.71 |
| 4 | $21,267.71 | $23,267.71 | $1,396.06 | $24,663.78 |
| 5 | $24,663.78 | $26,663.78 | $1,599.83 | $28,263.61 |
| 6 | ||||
| 7 | ||||
| 8 | ||||
| 9 | ||||
| 10 |
The year-5 interest figure ($1,599.83) has been corrected here: the source answer key prints $1,479.83 for that cell, which doesn't reproduce from $26,663.78 × 6%, but its own year-5 ending balance of $28,263.61 only works out correctly with the $1,599.83 figure, so that appears to be a simple typo in the original.
| Year | Value | After Deposit | Interest | New Amount |
|---|---|---|---|---|
| 6 | $28,263.61 | $30,263.61 | $1,815.82 | $32,079.43 |
| 7 | $32,079.43 | $34,079.43 | $2,044.77 | $36,124.20 |
| 8 | $36,124.20 | $38,124.20 | $2,287.45 | $40,411.65 |
| 9 | $40,411.65 | $42,411.65 | $2,544.70 | $44,956.35 |
| 10 | $44,956.35 | $46,956.35 | $2,817.38 | $49,773.73 |
If Peter invests $100 a year, from age 15 to 65, in a savings account compounding annually at 4%, how much will he have at 65? Formula each year: value after deposit = last year's new value + $100; interest = value after deposit × 4%; new value = value after deposit + interest.
| Age | New Value | After Deposit | Interest |
|---|---|---|---|
| 15 | $0.00 | $100.00 | $4.00 |
| 16 | $104.00 | $204.00 | $8.16 |
| 17 | $212.16 | $312.16 | $12.49 |
| 18 | $324.65 | $424.65 | $16.99 |
| 19 | $441.63 | $541.63 | $21.67 |
| … | … | … | … |
| 52 | $8,497.03 | $8,597.03 | $343.88 |
| 53 | $8,940.91 | $9,040.91 | $361.64 |
| 54 | $9,402.55 | $9,502.55 | $380.10 |
| 55 | $9,882.65 | $9,982.65 | $399.31 |
| 56 | $10,381.96 | $10,481.96 | $419.28 |
| 57 | $10,901.24 | $11,001.24 | $440.05 |
| 58 | |||
| 59 | |||
| 60 | |||
| 61 | |||
| 62 | |||
| 63 | |||
| 64 | |||
| 65 |
| Age | New Value | After Deposit | Interest |
|---|---|---|---|
| 58 | $11,441.29 | $11,541.29 | $461.65 |
| 59 | $12,002.94 | $12,102.94 | $484.12 |
| 60 | $12,587.06 | $12,687.06 | $507.48 |
| 61 | $13,194.54 | $13,294.54 | $531.78 |
| 62 | $13,826.32 | $13,926.32 | $557.05 |
| 63 | $14,483.37 | $14,583.37 | $583.33 |
| 64 | $15,166.70 | $15,266.70 | $610.67 |
| 65 | $15,877.37 | $15,977.37 | — |
Assessment: What questions would you ask a financial planner before investing $1,000 in a savings plan?
What do you need to consider before opening a savings account? What are its long-term benefits, and its short-term drawbacks?
Role-play: one student is an investment broker, the rest are investors asking questions (expected rate of return, safety, FDIC insurance, how long money must stay invested).
Students act as brokers advising one investor; use charts to demonstrate the best options. Brokers must determine the investor's risk tolerance first.
Role-play advisors helping a 25-year-old, financially stable client with $5,460 saved convert bank savings into an IRA. Build a three-stock portfolio matching their risk tolerance, project its value at retirement based on 5-year performance held steady for 40 years, compare that to leaving the money in a 4% bank account, and calculate the doubling time for each using the Rule of 72.
Enrichment: Build a personal financial plan contributing $5,000 a year to savings and stocks for twenty years, then use the funds to buy a house five years after the final contribution. Use 2% for savings and 12% for stocks. Explain how you'd split the funds and why, based on risk tolerance, career, family plans, and retirement timeline, then calculate what each side of the plan would be worth when it's time to buy.