Compound Interest Calculator

Calculate the compound interest of an initial investment based on interest rate and time in years. Annual, monthly compounding, etc. Formula and examples. Use a dot as the decimal separator.

Amount of money to invest (principal).
Amount of money you want to add each month.
Total duration of the investment.
Estimated annual interest rate.
%
How many times per year interest will be compounded.
Number of decimals to display.

Investment result

Future value =

Interest generated =

Return on investment =

Future value table (Vf)

Period
Future value
Contribution

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Simple Interest

What is compound interest?

Compound interest is a financial concept that describes how the value of an investment grows exponentially over time. Unlike simple interest, where interest is earned only on the principal amount, with compound interest, interest is earned on both the initial principal and the accumulated interest from previous periods. This results in faster growth of the investment over the long term.

How is compound interest calculated?

The calculation of compound interest takes into account several factors: the initial principal, the interest rate, the investment time, and the compounding frequency (how many times a year the interest is added to the principal). The more frequent the compounding, the higher the final return on investment.

Compound Interest Formula

Vf = P · (1 + r/n) nt

Where:

  • Vf = Future value of the initial principal.
  • P = Principal or initial amount invested.
  • r = Annual interest rate (in decimal)
  • n = Number of times interest is compounded per year
  • t = Number of years

Compound interest example

Suppose you invest $1000 in a savings account that offers a 5% annual interest rate, compounded monthly, for 5 years. In this way, we would have:

  • P = 1000 (initial principal)
  • r = 0.05 (5% in decimal)
  • n = 12 (monthly compounding)
  • t = 5 years
Vf = 1000 · (1 + 0.05/12)12·5
Vf = 1000 · (1.00416667)60
Vf = 1000 · 1.2834
Vf = 1283.4

After 5 years, the future value of your initial investment will be $1283.4. This means you have earned $283.4 in interest. If you had received simple interest, you would have only earned $250 ($50 per year). Compound interest has allowed you to earn an additional $33.4.

Applications and examples of compound interest

Compound interest plays a crucial role in many areas of personal finance and investing. Here are some examples of how it applies in real-life situations:

  • Retirement savings: Retirement savings accounts, such as 401(k) plans or IRAs, leverage the power of compound interest to grow savings over decades.
  • Long-term investments: Investors who hold stocks or mutual funds for long periods can benefit significantly from compound interest, especially if they reinvest dividends.
  • Credit card debt: Unfortunately, compound interest also works against you when it comes to debt. Credit card interest rates are often compounded daily, which can make debt grow quickly if not paid off.
  • Mortgages: Although mortgages generally use simple interest, prepayments can reduce the principal and, therefore, future interest, creating an effect similar to reverse compound interest.
  • Financial education: Understanding compound interest can motivate people to start saving and investing early, taking advantage of the power of time in their investments.