Simple interest vs compound interest
Simple interest pays the same rupee amount every period because it is always calculated on the original principal. Compound interest adds each period’s interest to the principal, so the next period’s interest is calculated on a larger base. The difference is small in year one and enormous by year twenty — which is why Einstein is (probably apocryphally) quoted calling compounding the eighth wonder of the world. This calculator shows both side by side for the same principal, rate and time, so the gap is visible in rupees rather than in theory.
Formulas
Simple interest: SI = P × R × T ÷ 100; Amount = P + SI
Compound interest: A = P × (1 + r ÷ n)^(n × t); CI = A − P
- P = principal, r = annual rate as a decimal, n = compounding periods per year, t = years
Example: ₹1,00,000 at 8% for 10 years. Simple interest = ₹80,000. Compounded yearly, the amount is 1,00,000 × 1.08¹⁰ = ₹2,15,892, so compound interest = ₹1,15,892 — ₹35,892 more than simple interest from exactly the same deal.
Does compounding frequency matter?
Less than people expect. The same ₹1 lakh at 8% for 10 years gives ₹2,15,892 with yearly compounding, ₹2,20,804 quarterly, ₹2,21,964 monthly and ₹2,22,535 daily. Going from yearly to daily adds about 3% to the final amount. The rate and the time horizon matter far more than the frequency, so when comparing two deposits, focus on the effective annual rate.
Where you meet each type
- Simple interest: short-term personal loans from friends, some gold loans, interest on delayed payments, savings-account interest quoted for a single month, and many exam problems.
- Compound interest: bank FDs and RDs (quarterly), PPF and EPF (yearly), mutual fund growth (continuous, in effect), credit-card debt (daily — which is why it is so expensive), and home loans (monthly, on the reducing balance).
The rule of 72 and the rule of 114
Divide 72 by the rate to estimate how many years money takes to double; divide 114 by the rate to estimate tripling. At 8%, doubling takes about 9 years and tripling about 14. The year-by-year table lets you verify these against exact figures.
Compounding works against borrowers too
On a credit card charging 3.5% a month, an unpaid ₹50,000 balance grows to about ₹75,600 in a year — an effective annual rate above 51%, not the 42% you get by multiplying 3.5 by 12. Enter 42% with monthly compounding in the calculator to see the effect. The same maths that builds wealth for a saver builds debt for a borrower, which is the strongest argument for clearing high-interest balances before investing.
Frequently asked questions
What is the compound interest formula?
A = P × (1 + r/n)^(n × t), where P is principal, r is the annual rate as a decimal, n is compounding periods per year and t is time in years. Compound interest = A − P.
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on principal plus previously earned interest, so it grows faster over time.