# Savings Interest Rate Calculator

**What Is A Savings Account**

An account with an interest imposed on the deposits is usually a savings account. The interest is your reward for depositing and not using the money over an extended period of time.

The bank usually invests the money and profits off of it, leaving you with a part of it in the form of interest. The most common way is to offer a smaller interest on the money deposited than on the money borrowed. This difference of interests is the profit of the bank and serves to keep the operations running in the long term.

Savings accounts are usually bound by a compound interest rate, hence we will be assuming that for the rest of the article.

**Calculating Your Savings Manually**

Savings are subjected to a lot of possible variables, be it interest rates, fees, continuous deposits and withdrawals, taxes, and many more.

For the sake of simplicity, we will assume that all of the costs are reflected in the interest rate of the deposit.

The **savings interest formula** then becomes a very simple compound interest formula.

As most savings accounts are working on the basis of yearly interest, we will be assuming the same situation in our formula.

The variables needed to successfully use the formula are as follows:

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

Principal | P | This is the money deposited by us, that will be yielding the interest. |

Yearly Interest Rate | r | This is the interest rate set by your bank as the yearly reward for keeping your savings with them. We assume the decimal version of the interest rate for our formula. |

Compounding Frequency | n | This indicates how often your sum compounds. This is usually done on a monthly basis, which is what we will assume for the formula below. |

Time | t | This is the duration of the investment expressed in years, as a decimal number. Hence, 2 years and 3 months would be 2.25 years, etc. |

The formula to calculate the value (V) of your investment after a given time is as follows.

V = P(1+\tfrac{r}{n})^{nt}

**Worked-out Example**

*Rita has invested $1,000 at a 6% yearly interest rate onto her savings account. Her account is compounded every 4 months. How much money will be in her account after 10 years and 9 months?*

First, we identify all of our variables.

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

P | 10,000 |

r | 6%, which is 0.06 in decimal form (simply divide the percentage by 100). |

n | 3, as compounding every 4 months implies 3 times a year. |

t | 10.75 as we have 10 whole years and then 9 out of 12 years, an equivalent of 0.75. |

We substitute these values and get the following.

V = P(1+\tfrac{r}{n})^{nt}

= 1,000(1+\tfrac{0.06}{3})^{3*10.75}

=1,000(1+0.02)^{32.25}

=1,000*1.02^{32.25}

=1,000*1.894 = \$1,894

Her investment will grow from $1,000 to $1,894 in 10 years and 9 months.