If you want to invest $3,448 over 23 years, and you expect it will earn 3.00% in annual interest, your investment will have grown to become **$6,804.93.**

If you're on this page, you probably already know what compound interest is and how a sum of money can grow at a faster rate each year, as the interest is added to the original principal amount and recalculated for each period.

The actual rate that $3,448 compounds at is dependent on the frequency of the compounding periods. In this article, to keep things simple, we are using an annual compounding period of 23 years, but it could be monthly, weekly, daily, or even continuously compounding.

The formula for calculating compound interest is:

$$A = P(1 + \dfrac{r}{n})^{nt}$$

- A is the amount of money after the compounding periods
- P is the principal amount
- r is the annual interest rate
- n is the number of compounding periods per year
- t is the number of years

We can now input the variables for the formula to confirm that it does work as expected and calculates the correct amount of compound interest.

For this formula, we need to convert the rate, 3.00% into a decimal, which would be 0.03.

$$A = 3448(1 + \dfrac{ 0.03 }{1})^{ 23}$$

As you can see, we are ignoring the n when calculating this to the power of 23 because our example is for annual compounding, or one period per year, so 23 × 1 = 23.

## How the compound interest on $3,448 grows over time

The interest from previous periods is added to the principal amount, and this grows the sum a rate that always accelerating.

The table below shows how the amount increases over the 23 years it is compounding:

Start Balance | Interest | End Balance | |
---|---|---|---|

1 | $3,448.00 | $103.44 | $3,551.44 |

2 | $3,551.44 | $106.54 | $3,657.98 |

3 | $3,657.98 | $109.74 | $3,767.72 |

4 | $3,767.72 | $113.03 | $3,880.75 |

5 | $3,880.75 | $116.42 | $3,997.18 |

6 | $3,997.18 | $119.92 | $4,117.09 |

7 | $4,117.09 | $123.51 | $4,240.61 |

8 | $4,240.61 | $127.22 | $4,367.82 |

9 | $4,367.82 | $131.03 | $4,498.86 |

10 | $4,498.86 | $134.97 | $4,633.82 |

11 | $4,633.82 | $139.01 | $4,772.84 |

12 | $4,772.84 | $143.19 | $4,916.02 |

13 | $4,916.02 | $147.48 | $5,063.50 |

14 | $5,063.50 | $151.91 | $5,215.41 |

15 | $5,215.41 | $156.46 | $5,371.87 |

16 | $5,371.87 | $161.16 | $5,533.03 |

17 | $5,533.03 | $165.99 | $5,699.02 |

18 | $5,699.02 | $170.97 | $5,869.99 |

19 | $5,869.99 | $176.10 | $6,046.09 |

20 | $6,046.09 | $181.38 | $6,227.47 |

21 | $6,227.47 | $186.82 | $6,414.30 |

22 | $6,414.30 | $192.43 | $6,606.72 |

23 | $6,606.72 | $198.20 | $6,804.93 |

We can also display this data on a chart to show you how the compounding increases with each compounding period.

As you can see if you view the compounding chart for $3,448 at 3.00% over a long enough period of time, the rate at which it grows increases over time as the interest is added to the balance and new interest calculated from that figure.

## How long would it take to double $3,448 at 3% interest?

Another commonly asked question about compounding interest would be to calculate how long it would take to double your investment of $3,448 assuming an interest rate of 3.00%.

We can calculate this very approximately using the Rule of 72.

The formula for this is very simple:

$$Years = \dfrac{72}{Interest\: Rate}$$

By dividing 72 by the interest rate given, we can calculate the rough number of years it would take to double the money. Let's add our rate to the formula and calculate this:

$$Years = \dfrac{72}{ 3 } = 24 $$

Using this, we know that any amount we invest at 3.00% would double itself in approximately 24 years. So $3,448 would be worth $6,896 in ~24 years.

We can also calculate the exact length of time it will take to double an amount at 3.00% using a slightly more complex formula:

$$Years = \dfrac{log(2)}{log(1 + 0.03)} = 23.45\; years$$

Here, we use the decimal format of the interest rate, and use the logarithm math function to calculate the exact value.

As you can see, the exact calculation is very close to the Rule of 72 calculation, which is much easier to remember.

Hopefully, this article has helped you to understand the compound interest you might achieve from investing $3,448 at 3.00% over a 23 year investment period.