Compare simple vs compound interest on the same principal, rate and time, with annual to daily compounding, to see both balances and the difference.
Simple vs Compound Interest Formulas
Simple interest is calculated only on the original principal:
Compound interest is calculated on the principal plus previously earned interest:
The signed difference between compound and simple balances is:
Variables:
- As is the ending balance with simple interest
- Ac is the ending balance with compound interest
- P is the original principal
- r is the stated nominal annual interest rate divided by 100
- n is the number of compounding periods per year
- t is time in years
Use comparison mode to see both ending balances, interest earned and their signed difference. The schedule shows selected milestones and the exact final time, rather than every year. Target-gap mode finds the first monthly checkpoint where the unrounded compound balance minus the simple balance is at least the entered USD target; it does not solve a continuous crossing time. Only months at or below the maximum time are tested. A blank maximum means 100 years, and a zero target first matches at time zero.
Both methods use the same nonnegative stated nominal annual rate and unchanged principal, with no deposits, withdrawals, payments, taxes or fees. Principal and target amounts are in USD. Fractional compounding periods use the power formula without rounding down; before the first full period, this model can put compound value below simple value. Actual accounts may handle partial periods differently. This is not an APR or APY comparison. Weekly means 52 periods and daily means 365 periods per model year, without calendar-date or leap-year adjustments.
Simple vs Compound Interest Comparison
The table below uses a $10,000 principal at 5% for both methods. Compound interest is calculated monthly.
| Time | Simple balance | Compound balance | Compound advantage |
|---|---|---|---|
| 1 year | $10,500.00 | $10,511.62 | $11.62 |
| 5 years | $12,500.00 | $12,833.59 | $333.59 |
| 10 years | $15,000.00 | $16,470.09 | $1,470.09 |
| 20 years | $20,000.00 | $27,126.40 | $7,126.40 |
| 30 years | $25,000.00 | $44,677.44 | $19,677.44 |
Example Problems
Example 1: Compare balances after 10 years.
You place $10,000 at 5% for 10 years. Simple interest gives:
As = 10,000(1 + 0.05 * 10) = $15,000.00.
Monthly compounding gives Ac = 10,000(1 + 0.05/12)120 = $16,470.09. Compounding adds $1,470.09 beyond the simple-interest balance.
Example 2: See the effect of a longer time horizon.
Using the same $10,000 and 5% rate for 30 years, simple interest reaches $25,000. Monthly compounding reaches $44,677.44, creating a $19,677.44 advantage.
Frequently Asked Questions
What is the main difference between simple and compound interest?
Simple interest is always based on the starting principal. Compound interest periodically adds interest to the balance, so later interest is earned on both the principal and prior interest.
Which method is better for savings?
With the same positive nominal annual rate and principal, compound value exceeds simple value after the first full compounding period in this model. They agree at that first period; before it, the fractional-power model can give a lower compound value. Whether an actual savings or borrowing product is favorable also depends on its rate definition, payment or deposit terms, fees, taxes and partial-period rules.
Does compounding frequency make a large difference?
For the same positive nominal annual rate, principal and time, more frequent compounding increases this model’s ending balance. The size of the difference depends on all those inputs. A quoted APY already incorporates compounding, so it should not be entered as though it were the stated nominal rate.
