When you take out a loan or open a savings account, the interest rate is usually represented as an annual interest rate or annual percentage yield. However, if you want to know how much interest you must pay or will earn over a shorter period of time, you must calculate the daily periodic interest rate.
Computation from the Annual Interest Rate
The annual interest rate equals the sum of the periodic rates over the period of one year. To calculate the daily periodic interest rate from the annual interest rate, divide the annual interest rate by 365, the number of days per year. For example, if you have an annual interest rate of 5.84 percent, divide 5.84 by 365 to find the daily periodic interest rate equals 0.016 percent.
Computation from the Effective Annual Interest Rate
The effective annual interest rate represents the interest earned over the course of the year after accounting for interest compounding. To calculate the daily periodic interest rate from the effective rate, first divide the effective rate by 100 to convert to a decimal. Next, add 1.0 and raise the result to the 1/365th power. Raising a number to a fractional power requires a scientific calculator or a computer program, such as Excel. Raising a number to the 1/365th power is the same thing as taking the 365th root of a number. The result equals the number that when multiplied by itself 365 times equals the original amount. Finally, subtract 1.0 and multiply the result by 100. For example, if the annual effective rate equals 6.0134 percent, divide 6.0134 by 100 to get 0.060134 and add 1.0 to get 1.060134. Next, raise 1.060134 to the 1/365th power to get 1.00016. Finally, subtract 1.0 to get 0.00016 and multiply by 100 to find the daily periodic interest rate equals 0.016 percent.
The daily periodic interest rate determines how much interest accrues on your account each day during the year, assuming the account calculates interest on a daily basis. This helps you better understand how the amount of interest you are charged — or that you earn on your savings — is calculated. Calculating the interest on your daily balance takes into account the changes in how much you owe or how much you have in your account.
Importance of Compounding
When a bank or other financial institution calculates interest on a daily basis rather than a monthly or yearly basis, the interest accrues at a faster rate. This occurs because the interest that is earned each day gets added to the account immediately so that on the second day, not only is the original deposit earning interest, but also the interest from the first day is also earning interest. With annual interest compounding, the interest earned the first day does not get added to the account until the end of the year.
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