Compound Interest: Growth, Contributions and Inflation

Compounding starts with money that remains invested

Principal is the starting money. If interest is retained, later interest can be earned on both principal and accumulated interest. Investor.gov describes this as compound interest. For a market investment, the same mathematical pattern is often used to model reinvested total returns, but the word “interest” does not make those returns contractually fixed.

A recurring contribution is different. It raises the account balance because new cash enters the account. To measure modeled growth, subtract both the starting amount and all later contributions from the final value. Counting new deposits as investment gains overstates what the assumed return produced.

Timing matters because money cannot earn modeled growth before it arrives. A deposit made at the start of a period has one more period to grow than the same deposit made at the end. MoneyBasis uses end-of-month contributions: growth on the opening balance first, then the deposit.SEC

The annual rate needs a compounding convention

MoneyBasis’s compound-interest calculator takes a nominal annual rate and a selected compounding frequency: annually, semiannually, quarterly, monthly or daily. If the nominal annual rate as a decimal is a and the selected frequency is k times a year, the effective annual growth factor is (1 + a/k)^k.

Monthly deposits still occur monthly even when another compounding frequency is selected. The model converts the selected frequency into an equivalent monthly growth factor, (1 + a/k)^(k/12). This keeps deposit timing consistent while preserving the chosen effective annual yield. It is a modeling convention, not a statement about when a particular bank credits interest.

A quoted effective annual yield already includes compounding. Entering it as a nominal rate with monthly compounding compounds it again. The APR/APY guide explains the conversion. The frequency control also does not create extra investment return; changing it while holding a nominal input fixed changes the effective yield assumption.CFPB

Example A: a lump sum with annual compounding

Start with $10,000, contribute nothing more and assume a 5% nominal annual rate compounded annually for ten years. The calculation is $10,000 × 1.05^10, producing $16,288.95. Contributions remain $10,000; the rest is modeled growth.

There is no evidence about future market performance in that multiplication. The example asks what follows if the rate applies every year. A real investment can have losses, varying returns and costs. The amount is also stated in future nominal dollars, before any adjustment for purchasing power.

Worked example

Example B: add $500 at each month end

Now start with $10,000, add $500 each month for twenty years, and use a 7% nominal annual return compounded monthly. The monthly rate is 0.07 ÷ 12. Each deposit has a different time to grow: the first earns growth for 239 subsequent months, and the last earns none before the final measurement.

Total contributed capital is $130,000.00: the initial $10,000 plus 240 deposits of $500. Final modeled value is $300,850.72, of which $170,850.72 is growth. The visual keeps these three series separate so the effect of contributions remains visible.

With a constant 3% inflation assumption, divide that final balance by 1.03^20. Its purchasing power is $166,573.75 in today’s dollars. This is another view of the same future balance, not an additional account balance to add to it.BLS

Example C: use zero return as a control

With $1,000 initially, $100 contributed at each month end and zero return for one year, the result is $2,200. All of it is contributed capital. That control isolates the saving effort from the assumed growth and is useful when the goal date is fixed.

Negative returns remain negative in MoneyBasis. A $1,000 lump sum with no deposits and a −12% nominal annual return compounded monthly becomes $886.38 after one year. That is a loss; it is not clipped to zero growth. The annual loss differs from exactly 12% because the monthly loss factor is compounded.

Contributions can make an account’s final balance exceed its starting balance even when investment growth is negative. Compare ending value with total contributed capital to distinguish that situation from a positive investment result.

Costs and an uneven path change the interpretation

Fees remove money that would otherwise remain invested, reducing both the current balance and the base for later growth. MoneyBasis does not apply an expense ratio, advisory fee, transaction fee or tax calculation separately. If the return input is intended to be after some costs, that assumption needs to be stated; a before-cost return and an after-cost return are different scenarios.SEC

Read the curve as a controlled experiment

The curve assumes a constant return, the chosen deposit timing and no withdrawals. Optional contribution increases take effect after each completed year. Increasing a contribution is an additional cash commitment, not an improvement in investment performance. Inflation is constant in the purchasing-power comparison, which does not estimate a household’s exact future spending basket.

A smooth curve contains no market shocks, recovery periods or behavioral interruptions. Lower and higher rates can show sensitivity, but they do not create confidence intervals. When deposits or withdrawals occur along the way, different return sequences can also produce different outcomes despite similar average returns. The retirement guide develops that distinction with explicit cash flows.

A practical reading order is contributed capital, assumed growth, then purchasing power. That sequence makes it easier to see which part of a result comes from controllable deposits and which part depends on uncertain inputs.