I would like to know..
Savings balance
Known rate
Interest rate
Main specifications
Initial savings
$
Annual interest rate
%
Time length
yrs
mos
Compound frequency
Monthly
Additional deposits
How much?
$
How often?
Monthly
When?
Beginning of period
Savings details
The Annual Percentage Yield (APY) is 1.947%.
Your final savings will be $8,761.89.
The sum of the additional deposits is $7,200; thus, your total principal (initial savings plus total additional deposits) is $8,200, and the total interest gained is $561.89.
Final balance breakdown as percentages
Balances
Represent
Bar graph

Savings Calculator

By Mateusz Mucha, Piotr Małek and Tibor Pal, PhD candidate

This Savings Calculator, also known as a savings account calculator, is a multifunctional tool that helps you to create a precise savings plan, so that you can save up enough money to buy your dream car or holiday. It works in various ways: you can either find out how much you'll save, how much your initial saving should be, or how much you need to deposit over a chosen period if you want to reach your saving goal. You can also estimate how much time does it take to save a desired amount and what interest rate you need to arrive at a given balance.

The real strength of this tool is that you can accurately model any situation. For example, in the advanced mode you can add the average inflation rate, which allows you to learn the purchasing power of your savings. There is also a dynamic graph where you can study your results visually. The Final Balance Breakdown and the chart of your Annual Balances provides you with the detailed balances, allowing you to follow the progress of your saving account easily over time.

Some practical notes on savings

As you probably already know, it is generally not a good idea to save money by putting it all under your mattress. Even if you want to put cash aside, there are multiple reasons to instead deposit it in a bank, or other financial institution, in the form of a bank account. A prominent reason for relying on such financial transactions is the fact that an interest rate is applied on your balance, which is usually higher than the inflation rate. In this way, your money are not only secured against possible thievery (and mice) but also protected against inflation. One of the drawbacks, however, is how accessible specific bank accounts make your money. To understand this, let's go through the most common types of bank account, which are the following:

  1. Current account or checking account

This type of account is the most liquid one, as you can access your money any time through multiple channels (i.e., debit card, withdrawal, writing a cheque). Usually, there is no or minimal interest paid on this kind of account.

  1. Savings account

You receive interest, but the bank limits the usage the funds to ATM withdrawal only.

  1. Time deposit or certificate of deposit (CD)

The deposited money is fixed in the account for a specific time, and the bank imposes a penalty for premature withdrawals. The longer the term, the higher the interest rate offered by the bank.

  1. Call deposit

A deposit account that allows for the withdrawal of funds without penalty, but requires a higher minimum balance to earn interest.

As you probably noticed, the degree of accessibility of your money and the interest rate offered are linked in the opposite manner (inversely proportional). In other words, the more you restrict your ability to use your money, the more interest you accumulate on your account.

The other benefit of keeping your money in a bank account is safety: your money is less exposed to market fluctuations than other investments, and is also secured by regulations. For example, many countries, including the U.S.A, implemented deposit insurance to protect bank depositors, in full or in part, from losses caused by the bank's failure to pay its debts when due. Of course, if you feel more confident and fancy high risk, high reward scenarios, you may instead choose to invest your money in a stock or bond market.

Savings calculator's specifications

Before you decide to open a savings account, you need to know how different factors affect your balance. Besides, to be able to apply this calculator properly, and to understand the equations that govern it, it is essential to get familiar with these specifications:

  • Initial deposit and desired savings

The opening balance is amount that you have when you open your account, and the final balance is the amount that you would like to reach. In financial terms, they are the present value and the future value, which are linked together by the time value of money, which is one of the most fundamental concept in finance. To learn more about how the present and future values are related in an investment, you may like to check out the IRR calculator.

  • Interest rate and APY

Interest rate is one of the most important factors when you are about to choose a saving account. It refers to the nominal interest rate, also known as simple interest (or the headline or quoted interest rate). When you look around different offers, however, you most probably see APY (Annual Percentage Yield), which is another type of rate often quoted for savings accounts. The power of APY is the fact that it incorporates the effect of compounding. Therefore, it removes one of the main drawbacks of the nominal interest rate. For your convenience, this calculator lets you choose which rate you would like to use.

  • Time length

It is the time frame that you decide to give up the use of your savings and put aside some money.

  • Compound frequency

Compound interest is one of the most powerful concepts in finance, and is present in most financial/investment products. In this context, compound interest might be defined as a gain that is earned not merely on the annual opening balance, but also on the previously earned interest. If interest is calculated on any prior interest, the more often interest calculations (compounding) occur, the more money you will earn. Eventually, this can have a significant effect on the final balance, especially in the long-term. The most simple compounding frequency is yearly, which means that interest is calculated on your balance annually. In this case, the nominal interest rate is equal to the APY. In practice, however, compounding occurs more often, for example, semi-annually or monthly, depending on the type of financial instrument and practice. Compounding may be applied even more frequently. Theoretically, it can reach its highest frequency, called continuous compounding, which is the mathematical limit of the procedure. For more insight into the background behind this, you can learn some interesting details in the Natural logarithm section of the log calculator.

  • Annual inflation rate

Since inflation can substantially change the buying power of an amount of money, it is essential to consider its effects. When the inflation rate is high, the real inflation-adjusted interest rate, or the real interest rate, on your balance is lower, which may not even compensate for the purchasing power loss caused by hikes in the general price level. In such a case, although in the nominal term you have a gain, in the real term, you lost on the transaction. You can include inflation rate in the advanced mode of this savings calculator.

  • Additional deposit

In this section, you may set a specific amount that you intend to add to your savings account during its term. Besides its amount (How much?), you can specify its regularity (How often?) and its timing (When?), which can be the beginning of or the end of the period. Also, you can set annual growth rate or periodic growth rate if you expect to put aside more money each year. The option to set a growth rate for the additional deposit allows you to model an anticipated increase in the money devoted to your savings, or to compensate for the purchasing power loss resulting from inflation.

How savings account calculator works

Our savings calculator has five distinct ways in which it can be used. This is done by setting the subject of your interest at the top of the tool, in the field titled "I would like to know..". These functions allow you to analyze your savings plan in multiple aspects, which are the following:

  1. What will be the final balance? - Savings balance
  2. What should the starting amount be to reach your savings target? - Initial deposit
  3. How much money should I put aside? - Additional deposit
  4. How long will it take to realize my desired savings? - Time length
  5. What should the interest rate on your savings account be to obtain sufficient amount of money? - Interest rate

Below we have set out two basic examples to represent the problems you may face when making a savings plan.

Firstly, let's say you are saving for your dream bike, and you would like to know how much money you need to put aside (additional deposit) to realize your dream:

  1. Find out the price of the bike. Let's say it is $2000 - and this is our desired savings that we want to achieve.
  2. Determine your initial deposit. Let's make it $1200.
  3. Find out the interest rate. We've found a savings account with a 1.93% interest rate.
  4. Last but not least, decide about the time length you want to save for. Let's say we are not in a hurry and can save over 2 years.
  5. Regarding the compounding frequency, you learn that the savings account you would choose is compounding monthly.
  6. Also, you set the frequency of your additional deposit to monthly, which occur at the end of the period.
  7. For simplicity, you don't count on inflation as you hope that the price of the bike will not change in such a short interval. You also do not choose to set an annual growth or periodic growth rate in the advanced mode for your additional deposits.
  8. By entering this data in our calculator, you will calculate that you only have to deposit $30.79 monthly to buy that bike in 2 years. Congratulations!

The other way to use the savings account calculator is to find out the initial deposit you need to put down (initial deposit) if you know how much we can deposit monthly:

  1. Determine the final savings balance. Let's make it $3000.
  2. Find out monthly additional deposit. Let's say we can deposit $120 monthly.
  3. Set the time length. Let's say 9 months is the deadline.
  4. Finally, enter the APY. Let's use 1.95% with a monthly compounding frequency.
  5. For simplicity, we will skip the setup for the inflation rate, annual growth and periodic growth rate again.
  6. By entering this data, you will find out that you will need to put down an initial deposit of $1883.78.

To see how your money will grow, you can study the monthly and yearly balances in a table at the bottom of the calculator, to check what makes up your final balance. We also created a bar chart, where you can visually follow the progression of your balances.

Note that the parameters of annual inflation rate and periodic/yearly growth rate of deposit can be found in the advanced mode.

Disclaimer

The results of this calculator, due to rounding, should be considered as just a close approximation financially. For this reason, and also because of possible shortcomings, the calculator is created for advisory purposes only.

Mateusz Mucha, Piotr Małek and Tibor Pal, PhD candidate

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