The Key Difference
Simple interest calculates interest from the original principal in the standard model. Compound interest allows previously credited interest to become part of the balance used for later periods.
Simple Interest Formula
P = principal, r = annual rate as a decimal, t = years.
The final amount is P + I.
Compound Interest Formula
n represents compounding periods per year.
Worked Comparison
Imagine the same 5,000 principal and 6% annual rate are modelled for several years. Under simple interest, the interest added each year is based on the original 5,000. Under compound interest, credited interest can increase the balance used for subsequent periods. The compound result therefore becomes progressively different from the simple-interest result as time passes.
Why the Gap Grows
Compounding creates a cumulative effect: interest that has already been credited can itself generate additional interest. The size of the difference depends on the rate, time horizon and compounding frequency.
Which Calculation Should You Use?
Use the method specified by the financial product or agreement. Do not choose compound or simple interest merely because one produces a more attractive result. If the terms are unclear, check the lender, bank or product documentation.
Common Mistakes
- Comparing results with different rates or time periods.
- Confusing nominal annual rate with the effective rate.
- Ignoring fees or taxes when comparing real products.
- Treating a mathematical investment projection as a guaranteed return.
Compare the Tervilo Calculators
Use the Simple Interest Calculator and Compound Interest Calculator to model the two methods using comparable assumptions.
Keep the Assumptions Consistent
A fair comparison uses the same principal, rate, time period and relevant compounding convention. Changing several inputs at once makes it difficult to identify why the results differ.
Simple Interest Example
With a principal of 5,000, a 6% annual rate and 3 years, simple interest is 5,000 × 0.06 × 3 = 900, producing a modeled total of 5,900.
Compound Interest Example
Using the same principal and annual rate, compound interest repeatedly applies the periodic rate to the accumulated balance. The result depends on the compounding frequency, so monthly and annual compounding can produce different totals.
Effective Rate and Nominal Rate
A stated nominal annual rate does not by itself describe the final effective growth when compounding occurs. Check the compounding frequency before comparing rates from different products.
Fees, Taxes and Product Terms
Mathematical interest is not necessarily the same as the amount retained from a real financial product. Fees, taxes, changing rates and product-specific rules can affect the actual outcome.
When Contributions Are Added
Regular deposits introduce additional principal over time. A simple one-time-principal formula should not be used as a complete model for a plan with recurring contributions.
Use the Tervilo Interest Calculators
Use the Simple Interest Calculator or Compound Interest Calculator after matching the assumptions to the calculation you need.
Keep the Assumptions Consistent
A fair comparison uses the same principal, rate, time period and relevant compounding convention. Changing several inputs at once makes it difficult to identify why the results differ.
Simple Interest Example
With a principal of 5,000, a 6% annual rate and 3 years, simple interest is 5,000 × 0.06 × 3 = 900, producing a modeled total of 5,900.
Compound Interest Example
Using the same principal and annual rate, compound interest repeatedly applies the periodic rate to the accumulated balance. The result depends on the compounding frequency, so monthly and annual compounding can produce different totals.
Effective Rate and Nominal Rate
A stated nominal annual rate does not by itself describe the final effective growth when compounding occurs. Check the compounding frequency before comparing rates from different products.
Fees, Taxes and Product Terms
Mathematical interest is not necessarily the same as the amount retained from a real financial product. Fees, taxes, changing rates and product-specific rules can affect the actual outcome.
When Contributions Are Added
Regular deposits introduce additional principal over time. A simple one-time-principal formula should not be used as a complete model for a plan with recurring contributions.
Use the Tervilo Interest Calculators
Use the Simple Interest Calculator or Compound Interest Calculator after matching the assumptions to the calculation you need.