Financial
Compound interest formula: project lump-sum growth across any compounding frequency
Calculate ending balance P * (1 + r/m)^(m*t) and total interest earned for annual, quarterly, monthly, or daily compounding.
The algebraic compound interest formula vs FV()
A lump-sum deposit P earning nominal annual rate r compounded m times per year for t years grows to P * (1 + r / m)^(m * t). This algebraic expression matches -FV(r/m, m*t, 0, P) to the penny without cash-flow sign confusion.
Investing $10,000 at 8% nominal annual interest compounded quarterly (m = 4, periodic rate 2%) for 5 years (20 quarters) yields $10,000 * 1.02^20 = $14,859.47—earning $4,859.47 in compound interest (vs $4,000 simple interest).
Assume a constant rate, no fees or taxes, and the stated compounding schedule. The loan example uses month-end payments. Effective annual rates require conversion rather than direct division by the number of periods. Real payment schedules can include rounding adjustments.
| Input (A) | Value (B) |
|---|---|
| Principal (P) | 10000 |
| Annual Rate (r) | 0.08 |
| Compounds / Year (m) | 4 |
| Years (t) | 5 |
Calculate ending balance and cross-check against FV
Subtracting B1 from the ending balance isolates pure interest earned ($4,859.47).
=ROUND(B1 * (1 + B2 / B3)^(B3 * B4), 2)Compare simple interest vs compound interest gain
Simple interest B1 * B2 * B4 gives $4,000.00, so compounding adds $859.47 of extra return.
=ROUND(B1 * (1 + B2 / B3)^(B3 * B4) - B1, 2)Try the example
Use the original values or change them to test your understanding.