# Compound Interest Calculator

Created by Luis Hoyos
Based on research by
Garrett, S. An Introduction to the Mathematics of Finance: A Deterministic Approach 2nd Edition (2013)See 1 more source
Cipra T. Financial and Insurance Formulas (2006)
Last updated: Jul 06, 2022

If you're searching for how to calculate compound interest, this compound interest calculator is what you need. With this tool, you can calculate the future value of your investment or loan.

Although this calculator asks for a yearly nominal interest rate, you can also use it to calculate daily compound interest if you assume one year equals one day.

## Compound interest formula

Mathematically, the compound interest formula is a function in which the future value grows exponentially with time:

FV = P (1 + r/m)ᵐᵗ

where:

• FV — the future value of the investment (in our compound interest calculator, it is the final balance);
• P — the initial balance (the present value of the investment);
• r — the annual interest rate (in decimals);
• m — the number of times the interest is compounded per year (compounding frequency)
• t — the number of years the money is invested.

Although FV grows exponentially with time, the same doesn't happen as m increases. The plot of FV vs. m is logarithmic, and there's a point where increasing the compounding frequency doesn't lead to significantly greater FV values.

## How to use this compound interest calculator

Now, let's see how to calculate compound interest using this calculator.

• Main inputs

1. Initial balance: refers to the amount of money to invest or deposit.
2. Interest rate: this term refers to the amount charged by the lender to the borrower. In this future value calculator, the interest rate is the yearly nominal interest rate (don't confuse it with the real interest rate). Still, you can calculate a daily compound interest if you assume one year = one day.
3. Term: how much time the interest rate will operate. In other words, how long the debt or your investment will last.
4. Compounding frequency: how often the compounding applies to your balance. For example:
• Semi-annually (2/Yr): a compounding frequency of two. For example, if your yearly nominal interest rate is 10%, a 5% interest rate will be applied twice during the year.
• Quarterly (4/Yr): a compounding frequency of four. For example, if your yearly nominal interest rate is 10%, a 2.5% interest rate will be applied four times during the year.
• Monthly (12/Yr): a compounding frequency of twelve. For example, if your yearly nominal interest rate is 10%, a 1% interest rate will be applied twelve times during the year.

1. How often - frequency of the additional deposits.
2. How much - the amount of the additional deposits.
3. When - the timing of the transaction of the additional deposit.
• Additional deposits at the beginning of the period are known as annuity dues. The rent paid at the beginning of each month is an example of an annuity due.
• Additional deposits at the end of the period are known as ordinary annuities. The interest payments from bonds are an example of an ordinary annuity.
4. Growth rate of deposit - For cases in which you predict your income will increase, for example, due to inflation or promotions.
Luis Hoyos
Initial balance
$Interest rate % Term yrs mos Compounding frequency monthly (12/Yr) Additional deposits How often? never Results The final balance is$4,926.8.
The total compound interest is \$3,926.8.
Balances
Represent
bar graph
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