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Mathematics
Compound interest — Why does growth accelerate?
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Compare simple and compound interest on the same principal with the same hypothetical rate per period. The Observations table provides the figures represented by the money bars and graph.
Period 0 is the start, before interest is added. Both methods have the same principal.
Choose Next period twice to see which amount earns interest.
Period 0 of 20
SimpleCompound
- Total balance (VND)
- Simple: 1,000,000Compound: 1,000,000
- Accumulated interest (VND)
- Simple: 0Compound: 0
- Interest this period (VND)
- Simple: Not yet earnedCompound: Not yet earned
Compound − simple balance
0 VND
Period 0 is the start, before interest is added. Both methods have the same principal.
Displayed amounts are rounded to the nearest VND (≈); calculations retain fractions. Rounded parts may differ from the rounded total.
Connection to sequences
S(k) = P(1 + kr)
C(k) = P(1 + r)k
P is the principal; r is the decimal rate per period (10% = 0.1); k counts elapsed periods, starting at 0. Simple interest adds the same Pr; compounding multiplies by the same 1 + r when P > 0.
Paused. Period 0: simple-interest balance 1,000,000 VND; compound-interest balance 1,000,000 VND.
Loading resourceModel notes
- One initial principal, with no further deposits or withdrawals. Both methods use the same hypothetical rate per period and equal-length periods. A period does not necessarily mean one year.
- Compound interest is added at the end of each period; the next period earns interest on the new balance. The simple-interest total includes earned interest, but only the original principal earns further interest.
- Negative or variable rates, fees, taxes, inflation and risk are excluded. The control ranges define the exploration, not current market rates or guaranteed returns.
- The graph shows balances at whole periods. Connecting lines and transitions illustrate the sequence, not fractional-period or continuous compounding. Rounding is for display only and does not follow any particular bank's rules.