Define a comparison that does not hide contributions
Each case begins with $5,000 and runs for 120 months. Deposits arrive at month-end. APY is treated as an effective annual rate; the equivalent monthly rate is (1 + APY)^(1/12) − 1. There are no fees, taxes, withdrawals, missed deposits or rate changes. The 2% and 4% rates are chosen scenarios, not current account offers.
| Case | Monthly deposit | Constant APY | Total contributed | Ending balance | Interest |
|---|---|---|---|---|---|
| Baseline | $250.00 | 2% | $35,000.00 | $39,244.18 | $4,244.18 |
| Larger deposit | $350.00 | 2% | $47,000.00 | $52,503.86 | $5,503.86 |
| Higher rate | $250.00 | 4% | $35,000.00 | $44,075.20 | $9,075.20 |
The larger balance is not all extra interest
Increasing the monthly deposit from $250 to $350 adds $13,259.68 to the ending balance. Of that, $12,000 is additional contributions; only $1,259.68 is additional modeled interest. Calling the whole improvement an “investment return” would misrepresent where the money came from.
Raising APY from 2% to 4% while leaving deposits unchanged adds $4,831.03. That difference is entirely modeled interest because the contribution schedule is identical. The larger-deposit case requires an extra $100 of monthly cash flow; the higher-rate case requires an account that actually maintains that rate on comparable terms. Neither condition should be assumed away.
Change the horizon and rerun the question
| Years | Baseline | Larger deposit | Higher rate |
|---|---|---|---|
| 1 | $8,127.40 | $9,338.36 | $8,254.61 |
| 5 | $21,275.12 | $27,577.01 | $22,628.02 |
| 10 | $39,244.18 | $52,503.86 | $44,075.20 |
| 20 | $80,987.64 | $110,410.79 | $101,916.05 |
Compounding gives the rate difference more time to act as the horizon grows. Meanwhile, the larger-deposit case continues to add more principal every month. This experiment compares these specific dollar and rate changes; it cannot establish that contributions always matter more than yield.
Reproduce all three cases
The preset links carry only a public example name. They do not expose a reader’s entered financial information. Keep contribution timing at month-end when reproducing this table. Changing it to the beginning of the month gives each deposit an additional month of growth.
A higher headline APY is not the whole account
Check fees, minimum balance requirements, rate conditions, access to cash and the possibility of future rate changes. The CFPB emergency-fund guide emphasizes safety and accessibility as well as saving behavior. It does not prescribe either rate used here.
A savings-account APY is not interchangeable with an assumed investment return. Securities can lose value, particularly over a short horizon; see the SEC’s risk-tolerance guidance. This article does not recommend moving an emergency reserve into risky assets to pursue the higher scenario.
Use the goal to choose the next question
If you have a deadline, ask the goal calculator for the required monthly deposit and compare it with a realistic budget. If you do not yet know the appropriate reserve target, start with the essential-expense worksheet. For rate conventions, the compounding guide explains the mathematics.
The formula retains precision internally and rounds display amounts to cents. The published case values are generated from the same pure model used in the automated tests. That makes the arithmetic reproducible; it does not make constant future APY a fact.
Calculation record and corrections
Methods, model boundaries and test cases are recorded in the October 31 calculation specification. Send a reproducible discrepancy, the page and the input values to contact@mycalcvault.com; do not send confidential account records.
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