Compound Interest Comparison: How to Compare Savings Plans

Comparing compound-interest scenarios side by side turns a vague "is this better?" into a single number: the ending balance. The formula is the same one used for a single investment, applied once per scenario, with the differences — rate, term, compounding, contributions — exposed as the only moving parts.

The single-scenario formula

Each scenario in a comparison uses the standard compound-interest formula for a principal plus optional recurring contributions:

balance = P(1 + r/n)^(n·t) + PMT × [((1 + r/n)^(n·t) − 1) / (r/n)]

The first term grows the principal P at annual rate r compounded n times per year for t years. The second term is the future value of a series of recurring contributions PMT made each compounding period — the ordinary annuity formula. Run this once per scenario and you have the numbers to compare.

What changes between scenarios?

The point of a comparison is to vary exactly one or two inputs and hold the rest fixed, so you can see what actually moves the needle. The usual levers: the annual rate (a high-yield account vs a market index assumption), the compounding frequency (monthly vs daily), the term (10 vs 30 years), and whether you add money monthly. Comparing two scenarios that differ in every input tells you nothing; comparing two that differ in one input tells you exactly what that input is worth.

Time is almost always the biggest lever because of the exponent (n·t). Doubling the term at a positive rate more than doubles the result, which is why the gap between a 20-year and a 30-year plan can be far larger than the gap between two interest rates.

Ordinary annuity vs annuity due (contribution timing)

Whether you contribute at the start or end of each period changes the result by one compounding period. Contributions made at the start of each period (annuity due) earn one extra period of interest, so the future value is multiplied by (1 + r/n):

annuity due = ordinary annuity × (1 + r/n)

For monthly contributions over many years this is a meaningful but not huge difference — it's the same as contributing one month earlier. The comparison tool lets you set the timing per scenario, so you can see exactly what "starting now" is worth versus "starting next month."

Effective APY: making rates comparable

Two scenarios with the same nominal rate but different compounding frequencies are not really the same rate. The effective annual percentage yield (APY) collapses any compounding frequency into one comparable number:

APY = (1 + r/n)^n − 1

A 6% nominal rate compounded monthly has an APY of about 6.17%; compounded daily, about 6.18%. The APY is what lets you compare a monthly-compounded savings account against a daily-compounded one without doing the full balance math. When two scenarios share an APY, their balances will match for the same principal and term.

Total contributions, total interest, and the "best"

For each scenario the comparison reports three numbers: the ending balance, the total you contributed (principal + all recurring payments), and the total interest earned (balance minus contributions). The interest is the part the bank or market paid you — the real return on the plan. Ranking scenarios by ending balance picks the "best," but ranking by interest earned can be more honest, because it strips out the money you simply put in yourself.

Try it yourself

The Compound Interest Comparison Calculator lets you line up to three scenarios side by side — each with its own principal, rate, compounding frequency, term, and optional recurring contribution with timing — and highlights the highest ending balance. For a single scenario, the Compound Interest Calculator does the same math for one plan, and the Retirement Calculator applies it to a long-horizon accumulation goal.