Calculate compound growth with initial principal, recurring contributions, distinct compounding frequencies, APY, year-by-year breakdowns, and scenario comparisons.
| Metric | Scenario A (Baseline) | Scenario B (Comparison) | Difference (B − A) |
|---|---|---|---|
| Ending Nominal Balance | — | — | — |
| Total Compound Interest Earned | — | — | — |
| Effective Annual Yield (APY) | — | — | — |
| Year | Starting Balance | Annual Contributions | Annual Interest | Ending Balance | Real Purchasing Power |
|---|---|---|---|---|---|
| 1 | $10,000.00 | $6,000.00 | $784.56 | $16,784.56 | $16,784.56 |
| 2 | $16,784.56 | $6,000.00 | $1,203.02 | $23,987.58 | $23,987.58 |
| 3 | $23,987.58 | $6,000.00 | $1,647.28 | $31,634.86 | $31,634.86 |
| 4 | $31,634.86 | $6,000.00 | $2,118.95 | $39,753.81 | $39,753.81 |
| 5 | $39,753.81 | $6,000.00 | $2,619.71 | $48,373.52 | $48,373.52 |
| 6 | $48,373.52 | $6,000.00 | $3,151.35 | $57,524.87 | $57,524.87 |
| 7 | $57,524.87 | $6,000.00 | $3,715.79 | $67,240.66 | $67,240.66 |
| 8 | $67,240.66 | $6,000.00 | $4,315.04 | $77,555.70 | $77,555.70 |
| 9 | $77,555.70 | $6,000.00 | $4,951.25 | $88,506.94 | $88,506.94 |
| 10 | $88,506.94 | $6,000.00 | $5,626.70 | $100,133.64 | $100,133.64 |
Compound interest grows both your initial principal and previously accumulated interest over time. This calculator computes ending nominal balance, total contributions, compound interest earned, Effective Annual Yield (APY), optional inflation-adjusted purchasing power, and a complete year-by-year growth schedule.
Given initial principal P, nominal annual interest rate r, and n compounding periods per year, the effective annual yield is APY = (1 + r/n)^n − 1. When recurring contributions C occur m times per year (monthly, quarterly, or annually) and m differs from n, the engine computes the exact equivalent periodic rate per contribution interval r_sub = (1 + r/n)^(n/m) − 1 so that compounding frequency and contribution frequency are never conflated.
An investor starts with $10,000 and contributes $500 at the end of each month for 10 years in an account earning 6% nominal annual interest compounded monthly (n = 12, m = 12).
Principal + Contributions: $70,000.00 ($10,000 initial + $60,000 contributions) | Total Interest Earned: $30,133.82 | Ending Balance: $100,133.82 | APY: 6.1678%.
Comparing $25,000 with $0 recurring contributions over 20 years at 5% nominal rate compounded annually (n = 1) versus compounded monthly (n = 12).
Annual compounding (APY 5.00%): $66,332.44 | Monthly compounding (APY 5.1162%): $67,816.01 — an extra $1,483.57 from compounding frequency alone.
For principal P and periodic contribution C made m times per year with effective periodic rate r_sub = (1 + r/n)^(n/m) − 1 over t years (N = m × t total contribution periods), the future value for end-of-period deposits is FV = P(1 + r/n)^(n×t) + C × [((1 + r_sub)^N − 1) / r_sub]. For beginning-of-period deposits, the contribution term is multiplied by (1 + r_sub).
The nominal annual rate does not reflect intra-year compounding. Effective Annual Yield (APY), calculated as (1 + r/n)^n − 1, measures the actual annual percentage return once intra-year compounding (such as monthly or daily compounding) is taken into account.
Many basic calculators inaccurately force compounding frequency and contribution frequency to be identical. PeekAndDo converts the nominal rate compounded n times per year into the exact equivalent rate for each contribution period m using r_sub = (1 + r/n)^(n/m) − 1, preserving mathematical accuracy across all combinations.
Inflation reduces the future purchasing power of money. If your investment grows at a nominal rate of 7% per year and you assume 2.5% annual inflation, a future nominal balance after t years is divided by (1 + 0.025)^t to express its value in today's constant dollars.