SOLVETUTORMATH SOLVER

Instrument MI-02-378 · Finance

Mutual Fund Calculator

State a starting sum, an expected gross return, the fund's expense ratio, and a horizon. The instrument compounds at the net rate and returns one number: what the position is actually worth.

Instrument MI-02-378
Sheet 1 OF 1
Rev A
Verified
Type 02 — Investing SER. 2026-02378

Future value after fees, $

$27,140.81

FV = P·(1 + (r − fee))ⁿ

The working Every figure verified twice
  1. fv = 10000·(1 + (12 − 1.5) ⁄ 100)^10 = 27,140.81
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

A mutual fund's expense ratio is not billed as a separate invoice — it is deducted from fund assets before the daily share price is set, so the return an investor sees already has the cost baked in. This instrument makes that deduction visible by treating it as a subtraction from the return itself: Expected gross annual return, % minus Annual expense ratio, % becomes the rate that actually compounds, year after year, on Initial investment, $. A retail saver comparing two options inside a 401(k) or IRA menu — an actively managed large-cap fund against a lower-cost index option — uses this to see what each fund's own disclosed cost turns a shared return assumption into, in dollars, not just in percentage points.

The fee sits inside the exponent rather than being subtracted once at the end because a fund's operating cost recurs every year, on whatever balance exists that year — not on the original principal alone. That is structurally different from a sales load, a one-time percentage some mutual fund share classes charge at purchase or redemption and settle immediately; a load shrinks the amount that starts compounding on day one, while an expense ratio shrinks the rate the balance compounds at for every year it stays invested. This sheet models only the second kind of cost, the one whose size is easiest to underestimate by eye.

Future value after fees, $ is nominal and assumes both Expected gross annual return, % and Annual expense ratio, % hold perfectly flat for the whole horizon, when real markets move unevenly and funds occasionally revise what they charge. It also tracks a single lump sum with no further contributions, ignores tax due whenever shares are eventually sold, and leaves out any sales load, portfolio trading cost, or account-level advisory fee layered on top of the expense ratio itself.

FV=P(1+rf100)nFV = P\left(1 + \frac{r - f}{100}\right)^{n}
FV — Future value after fees, $ · P — Initial investment, $ · r — Expected gross annual return, % · f — Annual expense ratio, % · n — Investment horizon, years. The ratio reduces the compounding rate every year, not the principal once.
  • Enter Initial investment, $ — the lump sum you're putting into the fund today.
  • Set Expected gross annual return, % to the return assumption you're testing, before any cost is removed.
  • Enter Annual expense ratio, % straight from the fund's prospectus fee table, not a rounded guess.
  • Set Investment horizon, years to how long the money stays in the fund untouched.
  • Read Future value after fees, $ — the balance the net rate actually compounds to over that stretch.

Worked example — $10,000 at a 1.5% expense ratio

Set Initial investment, $ to 10,000, Expected gross annual return, % to 12, Annual expense ratio, % to 1.5, and Investment horizon, years to 10. The net rate the balance actually compounds at is 12 minus 1.5, or 10.5% a year: 10,000 times 1.105 raised to the 10th power gives Future value after fees, $ of $27,140.81.

Compounding the same $10,000 at the unreduced 12% for ten years instead gives $31,058.48 — a gap of $3,917.67 that the 1.5% expense ratio alone accounts for. That gap is larger than a flat 1.5% times ten years of the principal would suggest, because the fee is removed from the rate every single year, so it also removes the growth those deducted dollars would otherwise have gone on to earn.

Questions

Why does a 1.5% expense ratio cost more than 1.5% of my money?

Because it is deducted from the growth rate every year, not from the principal once. On the calculator's own $10,000-at-12%-over-10-years setup, cutting the return by 1.5 points to 10.5% compounds to $27,140.81 instead of $31,058.48 — a $3,917.67 gap, larger than 1.5% times ten years of principal, since the dollars the fee removes each year would otherwise have kept earning returns of their own.

Does Annual expense ratio, % include the sales load my fund charges?

No. A sales load is a separate one-time percentage some mutual fund share classes charge at purchase or redemption and settle immediately, shrinking the amount that starts compounding on day one. Annual expense ratio, % is the fund's recurring operating cost, deducted from assets every year the position is held. This sheet models only the recurring cost; subtract a load from Initial investment, $ by hand before entering it.

Where do I find the real Annual expense ratio, % for a fund I'm weighing?

In the fund's prospectus or annual shareholder report, usually in a table titled Fees and Expenses or Annual Fund Operating Expenses, shown as a percentage of net assets. Most brokerage fund pages and screener tools publish the same figure next to the ticker. Use that disclosed number directly — rounding it to the nearest whole percent shifts Future value after fees, $ by more than the rounding looks like it should.

Is Expected gross annual return, % the fund's actual historical return?

Only if set to be. The field accepts any assumption — a fund's own long-run average, a benchmark index's historical figure, or a more conservative guess — and holds it fixed for every year of the horizon. Real annual returns vary considerably year to year, so Future value after fees, $ is what one steady assumption produces, not a forecast of what the fund will actually return.

How is this different from a calculator that works out the expense ratio itself?

A calculator that derives the expense ratio starts from a fund's raw dollar operating expenses and average assets and divides one by the other to reach the percentage. This instrument starts from an already-known percentage, pulled from the prospectus, and projects forward what that cost does to one investment over a chosen horizon. The two answer opposite questions — one measures the cost, the other spends it forward in time.

Does Future value after fees, $ include tax on the eventual sale?

No. The figure is pre-tax and nominal — it shows what the net rate compounds the principal to, with no allowance for capital gains tax due when shares are redeemed, no allowance for inflation eroding the purchasing power of that balance, and no allowance for any contribution made after the initial lump sum.

References

Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.