How much of a growing balance came from contributions rather than growth?

Define a balance ledger

Begin with columns for opening balance, external contribution, assumed growth, withdrawal, and closing balance. Keep the contribution timing explicit: start of period and end of period are different conventions. Use one convention consistently rather than changing it to match an attractive answer.

Investor.gov’s compound-interest calculator asks separately for an initial amount, contributions, time, estimated interest, and compounding frequency. Those inputs are a useful reminder that a growth illustration needs more than an annual percentage. The following worksheet is original and uses invented annual steps rather than a quoted savings product.

Calculate end-of-year contributions

Assume an initial $1,000, a fictional 5% annual growth factor for two years, and a $100 contribution at each year-end. Ignore fees, taxes, and withdrawals. Year 1 closes at $1,000 × 1.05 + $100 = $1,150. Year 2 closes at $1,150 × 1.05 + $100 = $1,307.50.

Total money supplied is $1,200: the opening $1,000 plus two $100 contributions. The difference of $107.50 is growth under these assumptions. Calling the entire $307.50 balance increase an investment gain would count the $200 of new contributions as earned growth.

Change only the contribution timing

Now add the same $100 at the start of each year. Year 1 becomes ($1,000 + $100) × 1.05 = $1,155. Year 2 becomes ($1,155 + $100) × 1.05 = $1,317.75. Money supplied remains $1,200, while calculated growth is $117.75.

The $10.25 difference between the two ending balances comes from the stipulated timing, not extra contributions or a higher assumed rate. With no contributions at all, the same fictional two-year factor produces $1,102.50. These three cases answer different questions and should retain different labels.

Read the assumed rate carefully

A constant 5% is a teaching input, not a current interest offer, expected market return, or promise. The arithmetic does not establish that any asset can produce the same return each year. If using a real statement, enter its actual cash flows and dates instead of forcing them into this simplified annual pattern.

Also distinguish a projected balance from a return measure. This worksheet reconciles a balance; it does not calculate a money-weighted return or compare managers. An irregular deposit schedule needs a method that actually accounts for those dates. A large deposit late in the period should not be treated as if it earned the whole year’s growth.

Method, sources, and limits

The examples were checked with decimal arithmetic and use only the stated fictional inputs. Investor.gov’s calculator page was opened on 26 October 2026; it supplies the input framework, not these results. No market series or customer account was used. The worksheet excludes uncertainty, fees, tax, and inflation and does not recommend a contribution amount or investment.