How to Calculate Bank Savings Interest

Sometimes, to calculate the interest earned from a savings account, we simply multiply the interest rate by the principal amount. However, in most cases, it is not so easy. For example, many savings accounts are listed with one-year interest rates but compounded monthly. Each month, a portion of interest will be calculated and added to the principal, affecting the interest of the following months. The gradual and continuous addition to principal is called compounding, and the easiest way to calculate future earnings is to use the compound interest formula. Read on to learn more about the pros and cons of this interest calculation.

Table of Contents

Calculate compound interest

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Identify the formula for calculating the effect of compound interest. That is:

A

=

P

(

first

+

(

r

n

)

)

n

*

t

{displaystyle A=P(1+({frac {r}{n}}))^{n*t}}

A=P(1+({frac {r}{n}}))^{{n*t}}

.

(P) is the principal amount, (r) is the one-year interest rate, and (n) is the number of times the interest is compounded during the year. (A) is the account balance calculated under the effect of compound interest.
(t) is the time the interest is accrued. This number should match the interest rate used (for example, if interest is calculated on an annual basis, then (t) should be the number or fraction of the year). If less than a year, divide the total number of months by 12 or the total number of days divided by 365.

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Specify the variable to use in the formula. Review personal savings account terms or contact a bank representative to enter a value into the equation.

Principal (P) is the initial deposit or existing funds used to calculate interest.
The interest rate (r) should be given as a decimal. 3% should be filled in the formula as 0.03. To get this number, you just need to divide 3 by 100.
The value (n) is the number of times interest is calculated and compounded to the principal (compounding) in a year. The most common is compounding monthly (n=12), quarterly (n=4) and yearly (n=1). However, there may still be other options, depending on the specifics of your savings account. ^{[1] X Research Source}

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Substitute the value into the formula. Once you’ve determined the value of each variable, fill in the compound interest formula to find the return over a specific time frame. For example, with P= 20,000,000, r=0.05 (5%), n=4 (quarterly compounded) and t=1 year, we have the following equation:

A

=

20,000,000 won

(

first

+

(

0

,

05

4

)

)

4

*

first

{displaystyle A=20,000,000(1+({frac {0.05}{4}}))^{4*1}}

A=20,000,000(1+({frac {0.05}{4}}))^{{4*1}}

copper.

The compounded daily interest is calculated in the same way, except that in this case the variable (n) is 365 instead of 4 as above. ^{[2] X Research Source}

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Do the calculation. Now that the value has been substituted, let’s solve the equation. Start by shortening the simple parts first. It involves dividing the annual interest rate by the number of periods to get the period interest (in this case,

0

,

05

4

=

0

,

0125

{displaystyle {frac {0.05}{4}}=0.0125}

{frac {0.05}{4}}=0.0125

) And find

n

*

t

{displaystyle n*t}

n*t

, here is simply:

4

*

first

{displaystyle 4*1}

4*1

. From this, we get the equation:

A

=

20,000,000 won

(

first

+

(

0

,

0125

)

)

4

{displaystyle A=20,000,000(1+(0.0125))^{4}}

A=20,000,000(1+(0.0125))^{{4}}

copper.

This equation can be further reduced by performing the calculation enclosed in brackets: $first$ $+$ $0$ $,$ $0125$ $=$ $first$ $,$ $0125$ ${displaystyle 1+0.0125=1.0125}$ $1+0.0125=1.0125$ . Now, we get: $A$ $=$ $20,000,000 won$ $($ $first$ $,$ $0125$ $)$ $4$ ${displaystyle A=20,000,000(1,0125)^{4}}$ $A=20,000,000(1,0125)^{{4}}$ copper.

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Solve the equation. Next, calculate the power by taking the result obtained in the last step to a power of four (that is,

first

,

0125

*

first

,

0125

*

first

,

0125

*

first

,

0125

{displaystyle 1.0125*1.0125*1.0125*1.0125}

1.0125*1.0125*1.0125*1.0125

). I can

first

,

051

{displaystyle 1,051}

1.051

. The equation is simply:

A

=

20,000,000 won

(

first

,

051

)

{displaystyle A=20,000,000(1,051)}

A=20,000,000(1,051)

copper. Multiply these two numbers together to get:

A

=

21.020,000 won

{displaystyle A=21,020,000}

A=21.020,000

copper. This is your savings account value after one year with 5% interest (compounded quarterly).

Note that this number is slightly higher than what you would expect to get when the annual interest rate is quoted – $20,000,000 won$ $*$ $5$ $%$ ${displaystyle 20,000,000*5%}$ $20,000,000*5%$ copper. It shows how important it is to understand how and when interest is compounded!
The profit earned is the difference between A and B. So the total profit is $21.020,000 won$ $-$ $20,000,000 won$ $=$ $1,020,000 won$ ${displaystyle 21,020,000-20,000,000=1,020,000}$ $21.020,000-20,000,000=1,020,000$ copper.

Calculate interest with regular capital contribution

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First, use the cumulative savings formula. You can also calculate the interest earned on your monthly capital contribution account. It is useful if the amount of money that you save is stable and is transferred to a savings account each month. The full equation is:

A

=

P

(

first

+

(

r

n

)

)

n

t

+

P

USA

BILLION

*

(

first

+

r

n

)

n

t

-

first

r

n

{displaystyle A=P(1+({frac {r}{n}}))^{nt}+PMT*{frac {(1+{frac {r}{n}})^{nt}-1} {frac {r}{n}}}}

A=P(1+({frac {r}{n}}))^{{nt}}+PMT*{frac {(1+{frac {r}{n}})^{{nt}}- 1}{{frac {r}{n}}}}

^{[3] X Research Sources}

Another simple method is to separate the compounding interest on the principal from the interest earned on the capital contribution (or payment/PMT). To get started, calculate principal interest using the cumulative savings formula.
As can be seen, with this formula, you can calculate the interest earned on the savings account that is deposited more monthly and compound interest by day, month or quarter. ^{[4] X Research Sources}

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Use the second component of the formula to calculate the return on equity. (PMT) represents the monthly capital contribution.

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Define variables. Check your savings or investment agreement for the following variables: principal “P”, annual interest “r”, and number of periods in year “n”. If not available, contact your bank. The variable “t” represents the number of years or parts of the year used to calculate the interest and “PMT” is the value of capital contribution/payment per month. “A” is the total account value obtained with a given time and capital contribution.

The principal “P” may also represent the account value at the selected time interest starts.
The “r” interest rate indicates the interest paid to the account each year. It should be expressed as a decimal in the formula. That is, a 3% interest rate should be expressed as 0.03. To get this decimal, you just take the interest rate as a percentage divided by 100.
“n” is simply the number of compoundings in a year. That would be 365 if compounded by day, 12 if by month, and 4 in case of quarter.
Similarly, “t” represents the number of years used to calculate interest. It can be the number of years or part of the year if the interest period is less than one year (eg 0.0833 (1/12) for a period of 1 month). ^{[5] X Research Sources}

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Substitute the value into the formula. With P=20,000,000, r=0.05 (5%), n=12 (monthly compounding), t=3 years and PMT=2,000,000 VND, we get:

A

=

20,000,000 won

(

first

+

(

0

,

05

twelfth

)

)

twelfth

*

3

+

2,000,000 won

*

(

first

+

0

,

05

twelfth

)

twelfth

*

3

-

first

0

,

05

twelfth

{displaystyle A=20,000,000(1+({frac {0.05}{12}}))^{12*3}+2,000,000*{frac {(1+{frac {0.05}{12 }})^{12*3}-1}{frac {0.05}{12}}}}

A=20,000,000(1+({frac {0.05}{12}}))^{{12*3}}+2,000,000*{frac {(1+{frac {0.05}{12 }})^{{12*3}}-1}{{frac {0.05}{12}}}}

copper.

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Simplify the equation. Start with shortening

r

n

{displaystyle {frac {r}{n}}}

{frac {r}{n}}

, which can be by dividing the interest rate of 0.05 by 12. We get:

A

=

20,000,000 won

(

first

+

(

0

,

00417

)

)

twelfth

*

3

+

2,000,000 won

*

(

first

+

0

,

00417

)

twelfth

*

3

-

first

0

,

00417

{displaystyle A=20,000,000(1+(0.00417))^{12*3}+2,000,000*{frac {(1+0.00417)^{12*3}-1}{0.00417 }}}

A=20,000,000(1+(0.00417))^{{12*3}}+2,000,000*{frac {(1+0.00417)^{{12*3}}-1}{0 ,00417}}

. You can also shorten it by adding one to the interest rate in brackets. The resulting equation will be:

A

=

20,000,000 won

(

first

,

00417

)

)

twelfth

*

3

+

2,000,000 won

*

(

first

,

00417

)

twelfth

*

3

-

first

0

,

00417

{displaystyle A=20,000,000(1,00417))^{12*3}+2,000,000*{frac {(1,00417)^{12*3}-1}{0.00417}}}

A=20,000,000(1,00417))^{{12*3}}+2,000,000*{frac {(1,00417)^{{12*3}}-1}{0.00417}}

copper

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Calculate exponentiation. First, find the exponent:

n

*

t

{displaystyle n*t}

n*t

. I can

twelfth

*

3

=

36

{displaystyle 12*3=36}

12*3=36

. Next, the power to reduce the equation to

A

=

20,000,000 won

(

first

,

1616

)

+

2,000,000 won

*

first

,

1616

-

first

0

,

00417

{displaystyle A=20,000,000(1,1616)+2,000,000*{frac {1,1616-1}{0.00417}}}

A=20,000,000(1,1616)+2,000,000*{frac {1,1616-1}{0.00417}}

copper. Simplify by subtracting by 1, we get

A

=

20,000,000 won

(

first

,

1616

)

+

2,000,000 won

*

0

,

1616

0

,

00417

{displaystyle A=20,000,000(1,1616)+2,000,000*{frac {0,1616}{0.00417}}}

A=20,000,000(1,1616)+2,000,000*{frac {0.1616}{0.00417}}

copper.

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Do the final calculations. Multiplying the first cluster of the equation, we get 32,320,000 VND. Calculate the remaining cluster by dividing the denominator by the numerator:

0

,

1616

0

,

00417

=

38

,

753

{displaystyle {frac {0.1616}{0.00417}}=38.753}

{frac {0.1616}{0.00417}}=38.753

. Next, multiply the result obtained by the value of contributed capital (in this case, 2,000,000 VND). The obtained equation is:

A

=

32,320,000 won

+

77,506,000 won

=

109.826,000 won

{displaystyle A=32,320,000+77,506,000=109,826,000}

A=32,320,000+77.506,000=109,826,000

copper. Savings account value with these terms will be

109.826,000 won

{displaystyle 109.826,000}

109.826,000 won

copper.

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Calculate the total profit earned. In this equation, the profit earned is the difference between the total account (A) and the sum of the principal (P) and the product between the number of times of capital contribution and the value of capital contribution (PMT*n*t). In the above example, the interest earned is equal to

109.826,000 won

-

20,000,000 won

-

2,000,000 won

(

twelfth

*

3

)

{displaystyle 109.826,000-20,000,000-2,000,000(12*3)}

109.826,000-20,000,000-2,000,000(12*3)

nice

109.826,000 won

-

20,000,000 won

-

72,000,000 VND

=

17,826,000 won

{displaystyle 109.826,000-20,000,000-72,000,000=17.826,000}

109.826,000-20,000,000-72,000,000=17.826,000

copper. ^{[6] X Research Source}

Use a spreadsheet to calculate compound interest

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Open a new workbook. Excel or similar spreadsheet programs (such as Google Sheets) save you time in calculations and even provide shortcuts in the form of pre-designed financial functions to help calculate compound interest.

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Set the variable name. When using spreadsheets, it’s always helpful to keep things as neat and clear as possible. Let’s start by naming the column the cells that contain important information used in your calculations (e.g. interest rate, principal, period, n, contributed capital).

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Put the variable in the spreadsheet. Now, fill in the account’s data in the next column. As a result, the spreadsheet is not only easy to view and interpret later, but it also allows one or more variables to be changed so that many different savings options can be studied.

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Make an equation. The next step is to type in your own version of the accrued interest formula (

A

=

P

(

first

+

(

r

n

)

)

n

*

t

{displaystyle A=P(1+({frac {r}{n}}))^{n*t}}

A=P(1+({frac {r}{n}}))^{{n*t}}

) or a more complex version, taking into account monthly contributions (

A

=

P

(

first

+

(

r

n

)

)

n

t

+

P

USA

BILLION

*

(

first

+

r

n

)

n

t

-

first

r

n

{displaystyle A=P(1+({frac {r}{n}}))^{nt}+PMT*{frac {(1+{frac {r}{n}})^{nt}-1} {frac {r}{n}}}}

A=P(1+({frac {r}{n}}))^{{nt}}+PMT*{frac {(1+{frac {r}{n}})^{{nt}}- 1}{{frac {r}{n}}}}

). Use any blank box, starting with “=” and using normal math notation (including brackets if necessary) to type the appropriate equation. Instead of entering variables like (P) and (n), type the names of the cells that store the corresponding data or simply click on those cells when composing the equation.

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Use the finance function. Excel also provides financial functions that can help with your calculations. In particular, “future value” (FV) can be used because it calculates the value of an account at some point in the future with variables like the ones you are familiar with. To use this function, go to any blank cell and type “=FV(“. Excel will have a tutorial window as soon as you open the first function formula bracket to assist in entering the correct parameters. ^{[7] ] X Research Source}

Instead of accumulating interest, the future value function is designed to calculate the amount to be paid to balance the existing account as it continuously accrues interest. Therefore, the function will automatically give a negative result. To resolve this issue, type $=$ $-$ $first$ $*$ $F$ $DRAW$ $($ ${displaystyle =-1*FV(}$ $=-1*FV($
Similar data parameters, separated by commas, are used in the FV function, but they are not exactly the same as the parameters we used above. For example, “interest rate” here is $r$ $/$ $n$ ${displaystyle r/n}$ $r/n$ (annual interest divided by “n”). It will be calculated automatically in the brackets part of the FV function.
The “nper” parameter here is the variable $n$ $*$ $t$ ${displaystyle n*t}$ $n*t$ – the total number of compounded interest periods and the total number of capital contributions. In other words, if the PMT is non-zero, the FV function will assume that you contribute the amount of PMT capital through each and every period specified by “nper”.
Note that this equation is most common for (calculations like) mortgage repayment over time with recurring payments. For example, if planning to pay monthly installments over 5 years, “nper” would be 60 (5 years * 12 months).
PMT is the amount of capital contribution periodically during the whole period (part of capital contribution per “n”).
“[pv]” (or Present Value) is the principal account – your account’s initial balance.
The last variable, “[type]” (type), can be left blank in this calculation (the function then returns itself to zero).
The FV function allows you to perform simple calculations inside the brackets of a function formula, such that a complete FV function might take the form $-$ $first$ $*$ $F$ $DRAW$ $($ $.05$ $/$ $twelfth$ $,$ $twelfth$ $,$ $2,000,000 won$ $,$ $100,000,000 VND$ $)$ ${displaystyle -1*FV(.05/12,12,2,000,000,100,000,000)}$ $-1*FV(.05/12,12,2,000,000,100,000,000)$ . It shows 5% annual interest compounded monthly for 12 month term and during that time you contribute 2,000,000 VND/month. At the same time, your initial balance (principal capital) is VND 100,000,000. The results obtained show how much your account has after 1 year (VND 129,674,000).

Advice

Besides, calculating compound interest may be more complicated with non-fixed capital contribution. At this point, you need to calculate the interest of each capital contribution/payment individually (with the same formula introduced above) and it is best to use a spreadsheet to simplify the calculation.
You can also use an online annual published interest calculator to determine the interest earned on a savings account. Search the internet for “annual interest calculator” for countless sites offering this free service.

Steps

Calculate compound interest

Calculate interest with regular capital contribution

Use a spreadsheet to calculate compound interest

Advice

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