Compound interest is the process where money earns returns, and then those returns earn more returns in later periods. This can feel like free money because growth begins to come not only from what you save, but also from what your past earnings add. For young investors, time is the biggest advantage because more years give compounding more cycles to work.
Even small regular investments can become large when they are left to grow for decades.
Key Facts
- Compound interest formula: A = P(1 + r/n)^(nt)
- Simple interest formula: A = P(1 + rt)
- Future value of monthly investments: FV = PMT[((1 + i)^N - 1)/i], where i is the monthly rate
- Rule of 72: doubling time ≈ 72/r, where r is the annual return percentage
- Monthly compounding grows faster than annual compounding when the stated annual rate is the same.
- Time in the market usually matters more than timing the market because missing early years reduces the number of compounding cycles.
Vocabulary
- Compound interest
- Compound interest is growth where both the original money and the previously earned interest or returns generate new earnings.
- Principal
- Principal is the original amount of money invested or saved before interest or returns are added.
- Rate of return
- Rate of return is the percentage gain or loss on an investment over a period of time.
- Compounding period
- A compounding period is how often earnings are calculated and added to the balance, such as monthly or annually.
- Rule of 72
- The Rule of 72 is a quick estimate that divides 72 by the annual percentage return to approximate how many years money takes to double.
Common Mistakes to Avoid
- Confusing compound interest with simple interest is wrong because simple interest grows only on the original principal, while compound interest grows on principal plus past earnings.
- Ignoring time is wrong because the earliest dollars invested usually have the most years to compound and can become the largest part of the final balance.
- Comparing monthly and annual compounding as if they are identical is wrong because more frequent compounding adds earnings to the balance sooner.
- Trying to perfectly time the market is wrong because waiting on the sidelines can remove years of compounding, and no one can reliably predict every market high and low.
Practice Questions
- 1 You invest $1,000 at 8% annual interest compounded annually for 10 years. Use A = P(1 + r)^t to find the final amount.
- 2 A student invests $100 per month from age 18 to 65 and earns an average annual return of 7%, compounded monthly. Using i = 0.07/12 and N = 47 × 12, estimate the future value with FV = PMT[((1 + i)^N - 1)/i].
- 3 Two students each invest the same total amount, but one starts at age 18 and the other starts at age 30. Explain why the earlier investor can end with more money even if both earn the same average return.