This saving calculator assists investors to learn the effects of compounding, it is capable to handle daily, weekly, monthly and annually compounding.

## Report

Year | Deposit($) at beginning | Interest ($) | Total Interest ($) | Principal + Interest($) |
---|---|---|---|---|

Annual ROI is

APR (Annual Percentage Rate) is

## Using the compound interest calculator

**Deposit**- Initial fund in your bank account.**Interest Rate**- Annual interest rate.**Years**- The duration of investment (e.g. 5 years).**ROI**- Return on investment.

## What is Compound Interest and how to calculate it

Compound interest is different from the simple interest because the interest is included in principal periodically.

Let’s see an example:

principal is $1000 at beginning, annual interest rate is 3%. What is the interest for the next three years?**Simple Interest**:

Interest of each year is $1000 * 3% = $30.

Total simple interest for three years is: $30 + $30 + $30 = $90. **Compound Interest**:

Let’s assume compound period is one year, which means interest earned in a year will be added to principal at the end of the year. What a great news! The interest earned in the previous year will start to make money in the following years.

- 1
^{st}year compound interest is $1000 * 3% = $30

principal at the beginning of 2nd year is $1000 + $30 = $1030. - 2
^{nd}year compound interest is $1030 * 3% = $30.90

Principal at the beginning of 3rd year is $1030 + 30.90 = $1060.90 - 3
^{rd}year compound interest is $1060.90 * 3% = $31.83

After 3 year, $1000 grows to $1092.73. Compound interest for three years is: $30 + $30.90 + $31.83 = $92.73.

## Compound Interest Formula

The essential factors of calculating compound interest are principal, interest rate and frequency of compounding in a given duration.

The calculation formula is: **compound interest = P * (1+r/n) ^{nt} - P**

- P is principal or the original deposit in bank account.
- r is the annual interest rate.
- t is the number of years.
- n is number of times the interest is compounded in a year.

## Simple interest *vs* compound interest

In simple interest, only principal makes money(earns interest), whether your investment lasts one year or ten years.

In compound interest, not only principal earns interest, but also interest earned in previous period will earn interest in the following periods. Compound interest is used more popularly in our real life, like credit card, saving and checking account, and mortgage loan.

For example, **$10,000 at 8% annual interest rate, compounded annually for 10 years**. Calculate its simple interest and compound interest.

Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

Annual simple interest | $800 | $800 | $800 | $800 | $800 | $800 | $800 | $800 | $800 | $800 |

Annual compound interest | $800 | $864 | $933.12 | $1,007.77 | $1,088.39 | $1,175.46 | $1,269.50 | $1,371.06 | $1,480.75 | $1,599.20 |

Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

Total simple interest | $800 | $1,600 | $2,400 | $3,200 | $4,000 | $4,800 | $5,600 | $6,400 | $7,200 | $8,000 |

Total compound interest | $800 | $1,664 | $2,597.12 | $3,604.89 | $4,693.28 | $5,868.74 | $7,138.24 | $8,509.30 | $9,990.05 | $11,589.25 |

Below chart explains visually the differences between simple interest calculation and compound interest calculation.