1,000 at 2% a month for 12 months (simple | compound)
- Input
- 1000 | 2% | 12
- Expected output
- 1240,00 | 1268,24
A gap of 28.24, or 11.8% more interest than simple (28.24 over 240).
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simple vs compound interest difference
The difference between the regimes is just one thing: with simple interest the rate always applies to the original principal; with compound it applies to the previous period's amount, interest on interest. Small at first, large over the long run. The Simple vs compound tab draws both curves and the period-by-period table.
A gap of 28.24, or 11.8% more interest than simple (28.24 over 240).
Compound passed 100% gain; simple stayed at 72%.
At t = 1 they are equal. At t = 2 compound already earns 0.40 more.
A gap of 1,623.42. With compound interest, 12% a year also equals 0.9489% a month, not 1%.
I = P × r × t, where P is the principal, r the rate per period (as a decimal, 2% = 0.02) and t the number of periods, always in the same unit as the rate. The amount is A = P + I = P × (1 + r × t). Example: 1,000 at 2% per month for 6 months earns I = 1,000 × 0.02 × 6 = 120, and the amount is 1,120.
In exams, in informal loans between people, in discounting notes and invoices, and in pro rata late interest per day of delay. Loans, cards and most investment products usually use compound interest. When in doubt, check the contract for the regime and day-count basis.
With a positive rate, yes, for any time over 1 period; at t = 1 they tie and below 1 period simple earns more (under the exponential convention). With a negative rate, compound loses less. With a zero rate they are equal.
It depends on the rate and on what you call relevant. At 2% a month, the gap passes 1% of the principal in month 8 and compound interest sits 10% above simple in month 11. The calculator reports these points for your rate.