Learning Labs / Compound Interest & Inflation Lab
Small changes. Long-term lessons.
Explore how time, contributions, interest, and inflation change the value of money.
Lesson 01 / Build your understanding
Simple vs compound interest
Explain why compound growth accelerates while simple interest adds a fixed amount to unchanged principal.
01 / Concept
Start with the idea.
Simple interest earns interest on deposited principal. Compound interest adds interest to the balance, so later interest can earn interest too.
With 1,000 at 10% once a year, both reach 1,100 after year one. In year two, simple interest adds another 100; compound interest earns 10% of 1,100, adding 110.
Read the reasoning
Our simple comparison applies the selected stated annual rate only to deposited money. Compound scenarios also respect the selected annual-rate basis and compounding frequency. Recurring contributions use identical dates in both models.
Key terms
- Principal
- Money deposited, separate from the interest it earns.
- Compound growth
- Growth applied to a balance that includes earlier interest.
02 / Predict
What do you expect?
Follow the money, not just the total.
Change one assumption, run the scenario, and separate deposits from growth.
The lower shaded area is deposited money; the band above it is nominal growth. The dashed real-value line uses today's money. At small widths, scroll the chart or inspect the table.
Month 120: $2,593.74 balance; $20.52 growth earned during this month; $0.00 deposited at this boundary.
Read the change and its cause.
Simple interest applies the selected stated annual rate only to deposited principal. Compound growth also applies to earlier interest; both scenarios use the same deposits and dates.
Your nominal result is $2,593.74; simple interest ends at $2,000.00. Difference: $593.74.
EAR = (1 + 0.1/1)^1 − 1 = 10%
Monthly rate q = (1 + EAR)^(1/12) − 1 = 0.7974%
Month 120 interest = $2,573.22 × 0.7974% = $20.52
Closing balance = opening balance + growth + deposit at that boundary.
j = (1 + q)^1 − 1 = 0.7974%; n = 120 contribution periods.
FV = $1,000.00 × (1 + q)^120 + $0.00 × ((1 + j)^n − 1) / j = $2,593.74.
Real balance = $2,593.74 ÷ (1 + 0)^10 = $2,593.74
Real annual rate = (1 + 0.100000) ÷ (1 + 0) − 1 = 10%
Why nominal deposits are not a real-profit baseline
Nominal deposits total $1,000.00. Discounting each contribution to today's money at its arrival date gives $1,000.00. Real growth above those discounted deposits is $1,593.74. Comparing real balance directly with the raw nominal deposit sum would mix two different value bases.
Inspect period-by-period values
| Month / year | Total deposited | Nominal growth | Nominal balance | Today's purchasing power |
|---|---|---|---|---|
| 0 / 0 | $1,000.00 | $0.00 | $1,000.00 | $1,000.00 |
| 12 / 1 | $1,000.00 | $100.00 | $1,100.00 | $1,100.00 |
| 24 / 2 | $1,000.00 | $210.00 | $1,210.00 | $1,210.00 |
| 36 / 3 | $1,000.00 | $331.00 | $1,331.00 | $1,331.00 |
| 48 / 4 | $1,000.00 | $464.10 | $1,464.10 | $1,464.10 |
| 60 / 5 | $1,000.00 | $610.51 | $1,610.51 | $1,610.51 |
| 72 / 6 | $1,000.00 | $771.56 | $1,771.56 | $1,771.56 |
| 84 / 7 | $1,000.00 | $948.72 | $1,948.72 | $1,948.72 |
| 96 / 8 | $1,000.00 | $1,143.59 | $2,143.59 | $2,143.59 |
| 108 / 9 | $1,000.00 | $1,357.95 | $2,357.95 | $2,357.95 |
| 120 / 10 | $1,000.00 | $1,593.74 | $2,593.74 | $2,593.74 |
Month 0 includes the first recurring deposit only for beginning schedules. At later boundaries, beginning deposits fund the next contribution period; there is no new beginning deposit at the final horizon. The first contribution for an end schedule arrives after its first complete period.
Scenario assumptions: constant rates and prices, uniform months, and smooth monthly growth equivalent to the selected compounding frequency. Actual credit dates and day-count conventions can differ. No fees, taxes, withdrawals, or uncertain returns are modeled. These figures illustrate the math; they do not promise investment outcomes.
05 / Practice
Put the idea to work.
06 / Recap
Take the lesson with you.
- Simple interest uses deposited principal; compound interest also grows earlier interest.
- Keep deposits, dates, and rate assumptions equal when comparing.
- Separate deposited money from growth before interpreting the final balance.
Check your prediction and solve a practice challenge to complete this lesson.
References & further reading
Keep your curiosity going.
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