# How Long Will it Take to Save? Calculator

## Why Use This Calculator

Saving up towards a certain goal is always a difficult task requiring some preparation and discipline. Our calculator allows you to calculate the duration needed to save your desired sum of money, based on the following criteria that you can choose from:

Prerequisite | Explanation |
---|---|

1 | Currency you are operating in. |

2 | The current balance on your account (the money you have already managed to save). |

3 | Your savings goal (the sum you are aiming at saving). |

4 | The size of the deposits you will be making regularly. |

5 | The frequency of your deposits (usually tied in with the frequency of your pay). |

6 | The annual interest rate at your savings or current account. |

## Calculating The Time Needed To Save A Certain Amount

Calculating the duration needed to save a certain sum can be fairly simple if interest is not involved.

However, most accounts offer some form of simple or compound interest, which increases the value of your savings over time. Using this kind of account makes it quicker for us to save our desired amount, but also more complicated to do said calculations on our own. If you wish to not use our calculator, and calculate the duration manually, you can follow the following guide and formula, which is one of the examples of how the duration can be calculated in a relatively simple manner.

In our formula to calculate the duration it will take to save up to our goal (T), we will require the following data:

Symbol | Explanation |
---|---|

C | Our current balance |

G | Our savings goal |

D | Regular deposits we plan to make |

n | The frequency of our deposits |

r | The interest rate on our account |

Once we have this information available, we can substitute the values into the following formula.

T=\cfrac{(G-C)}{D*(1+\cfrac{r}{n*100})}

The result of this formula will give us a value in terms of “n”, which means, that if our deposits were weekly, then our result is the number of weeks. If our deposits were monthly, then the result is the number of months, etc.

We have to keep in mind, that in order to calculate the results properly within a real-life context, we have to always round the result up to the nearest whole number if any decimal part is present.

There are many possible factors that could change the formula slightly, such as using compound interest instead of simple, having our interest compounded at a different frequency than a yearly one, or simply having no interest involved at all. The formula offered is just an example.

### Worked Out Example

Jocey is trying to save up $5,000 for a car. She currently has $1,200 saved up. Her current employer is paying her $2,000 a month, out of which she will be depositing a quarter each month towards the car savings. Her current account offers a 12% annual simple interest rate.

We summarize the values we have.

Symbol | Value |
---|---|

C | 1,200 |

G | 5,000 |

D | 2,0004 = 500 (because she is depositing a quarter of her paycheck each month) |

n | 12, since it is monthly, hence 1/12 of a year. |

r | 12% |

We see that our deposits are monthly, hence our result will be in months. We plug in the values and get the following.

T=\cfrac{(G-C)}{D*(1+\cfrac{r}{n*100})}

=\cfrac{(5,000-1,200)}{500*(1+\cfrac{12}{12*100})}

=\cfrac{(3,800)}{500*(1.01)}

=\cfrac{(3,800)}{505}=7.52

This means, that if we round the value up to 8 months, we get that it will take her 8 months to save up for the car, knowing that her final savings will exceed $5,000.

Keep in mind, that our calculator is much more accurate, as it takes into consideration the continuous increase in value of the money already saved. Using such a formula is very complicated, hence we recommend using the calculator instead.

T=\\\cfrac{\log\left(\cfrac{(G-Dn)rn+Dr(n^{-1})+D(n^{-1})}{Crn+Dr(n^{-1})+D(n^{-1})} \right)}{D*\log(1+\cfrac{r}{n})}

For informative purposes, the said formula is as follows.

Using the advanced formula usually yields a result, that is a bit shorter, as the evaluation of our savings makes the process faster.