(P) is the principal (P), (r) is the annual rate of interest, and (n) is the number of times the interest is compounded per year. (A) is the balance of the account you are calculating including the effects of interest. (t) represents the periods of time over which the interest is accumulating. It should match with the interest rate you are using (e. g. if the interest rate is an annual rate, (t) should be a number/fraction years). To determine the appropriate fraction of years for a given time period, simply divide the total number of months by 12 or divide the total number of days by 365.
The principal (P) represents either the initial amount deposited into the account or the current amount that you will be measuring from for your interest calculation. The interest rate (r) should be in decimal form. A 3% interest rate should be entered as 0. 03. To get this number, simply divide the stated percentage rate by 100. The value of (n) is the number of times per year the interest is calculated and added onto your balance (aka compounds). Interest most commonly compounds monthly (n=12), quarterly (n=4), or yearly (n=1) but there can be other options, depending on your specific account terms. [2] X Research source
Interest compounded daily is found in a similar way, except you would substitute 365 for the 4 used above for variable (n). [3] X Research source
This is then further simplified by solving for the object within the parenthesis, 1+0. 0125=1. 0125{\displaystyle 1+0. 0125=1. 0125}. The equation will now look like this: A=$1000(1. 0125)4{\displaystyle A=$1000(1. 0125)^{4}}.
Note that this is slightly higher than $1000∗5%{\displaystyle $1000*5%} that you may have expected when the annual interest rate was quoted to you. This illustrates the importance of understanding how and when your interest compounds! The interest earned is the difference between A and P, so total interest earned =$1051−$1000=$51{\displaystyle =$1051-$1000=$51}.
An easy approach is to separate the compounding interest for the principal from that of the monthly contributions (or payments/PMT). To begin, calculate the interest on the principal first using the accumulated savings formula. As has been described with this formula, you can calculate the interest earned on your savings account with recurring monthly deposits and interest compounded daily, monthly or quarterly. [5] X Research source
The principal “P” represents either the balance of the account on the date that you will be starting the calculation from. The interest rate “r” represents the interest paid on the account each year. It should be expressed as a decimal in the equation. That is, a 3% interest rate should be entered as 0. 03. To get this number, simply divide the stated percentage rate by 100. The value of “n” simply represents the number of times the interest is compounded each year. This should be 365 for interest compounded daily, 12 for monthly, and 4 for quarterly. Similarly, the value for “t” represents the number of years you will be calculating your future interest for. This should be either the number of years or the portion of a year if you are measuring less than a year (e. g. 0. 0833 (1/12) for one month). [6] X Research source
The future value function is designed with paying an account balance down as it continues to accumulate interest instead of with accumulating savings account interest. Because of this it automatically yields a negative number. Counteract this issue by typing =−1∗FV({\displaystyle =-1FV(} The FV function takes similar data parameters separated by commas but not exactly the same ones. For instance, “rate” refers to r/n{\displaystyle r/n} (the annual interest rate divided by “n”). This will calculate automatically from within the FV function’s parenthesis. The parameter “nper” refers to the variable n∗t{\displaystyle nt} - the total number of periods over which interest is accumulating and the total number of payments. In other words, if your PMT is not 0, the FV function will assume you are contributing the PMT amount across each and every period as defined by “nper”. Note that this function is most often used for (things like) calculating how a mortgage principal is paid down over time by regular payments. For instance if you plan to contribute every month for 5 years, “nper” would be 60 (5 years * 12 months). PMT is your regular contribution amount over the entire period (one contribution per “n”) “[pv]” (aka Present Value) is the principal amount - your account’s starting balance. The final variable, “[type]” can be left blank for this calculation (when it is the function sets it automatically to 0). The FV function allows for you to do basic calculations within the function parameters, for instance the completed FV function could look like −1∗FV(. 05/12,12,100,5000){\displaystyle -1*FV(. 05/12,12,100,5000)}. This would signify a 5% annual interest rate which compounded monthly for 12 months, over which time you contribute $100/month and your starting (principal) balance is $5000. The answer to this function will tell you the account balance after 1 year ($6483. 70).
