Compound Interest Calculator
Enter the principal, the yearly rate, how often it compounds and the time to get the future value from A = P × (1 + r ÷ n)^(n × t), the interest, the effective yearly rate, the doubling time and the balance year by year. Continuous compounding is included.
- Working100,000 × (1 + 0.15 ÷ 12)^(12 × 10) = 444,021.32
- Interest earned (A − P)344,021.32 ₺
- Effective yearly rate16.08%
- With simple interest250,000.00 ₺
- Years to double4.65
- Interest on interest (compound − simple)194,021.32 ₺
Growth by year
How it is calculated
With compound interest, the interest earned each period is added to the principal and earns interest in turn, so money grows exponentially. More frequent compounding raises the result, but only up to a limit: continuous compounding, P × e^(r × t). This page works the school formula step by step at a fixed rate and leaves out tax, fees and inflation. For the net return on a Turkish term deposit, use the deposit interest calculator; to compare simple and compound interest over days, months or years, use the finance interest calculator.
A = P × (1 + r ÷ n)^(n × t) · A = P × e^(r × t)A: future value · P: principal · r: yearly rate (15% → 0.15) · n: compounding periods a year (monthly 12) · t: time in years · e ≈ 2.71828. The second formula is continuous compounding.- Find the rate per period: r ÷ n (15% a year compounded monthly: 0.15 ÷ 12 = 0.0125).
- Find the number of periods: n × t (10 years monthly: 120 periods).
- Raise (1 + the period rate) to the number of periods and multiply by the principal.
- The interest earned is the future value less the principal: A − P.
Example
₺100,000 at 15% a year compounded monthly for 10 years: A = 100,000 × (1 + 0.15 ÷ 12)^120 = 100,000 × 1.0125^120 ≈ ₺444,021.32, so ₺344,021.32 of interest. The effective yearly rate is (1.0125)^12 − 1 ≈ 16.08%. Compounded continuously it becomes 100,000 × e^1.5 ≈ ₺448,168.91.
Frequently asked questions
What is the rule of 72?
To estimate how long money takes to double, divide 72 by the rate in percent: at 15%, 72 ÷ 15 = 4.8 years. The exact time is ln 2 ÷ ln(yearly growth): about 4.96 years compounded yearly and 4.65 years monthly. The rule is closer at low rates.
How much does more frequent compounding add?
At 15% nominal the effective yearly rate is 15% compounded yearly, 16.08% monthly, 16.18% daily and e^0.15 − 1 ≈ 16.18% continuously. Going from monthly to daily changes little; continuous compounding is the ceiling.
What is the effective yearly rate?
The rate at which money actually grows in a year: (1 + r ÷ n)^n − 1. It lets you compare rates that compound at different frequencies.
What is continuous compounding?
It is the limit as compounding becomes infinitely frequent (n → ∞): A = P × e^(r × t), where e ≈ 2.71828 is Euler’s number. It is rare in practice but basic in financial maths and growth models.
How do I allow for inflation?
The real return is (1 + nominal rate) ÷ (1 + inflation) − 1: at 15% interest and 10% inflation, about 4.55%. To use actual Turkish CPI data, use the real return calculator.