Nominal Rate vs. Effective Rate

Time and money are related.

The effective interest rate is the actual rate of interest when the interest is compounded, in a savings account, for example. This means that the interest gained during one period joins the savings for the next period. When dealing with the yearly interest rate, the difference between the nominal and effective rates comes into play whenever the interest is compounded more than once per year. The nominal yearly rate is the raw interest, or the interest without compounding.

Nominal Rate

The nominal yearly interest rate is the yearly rate of interest without compounding. If you pull out the interest gained instead of reinvesting it, you will earn the nominal rate. Its better use is to calculate the rate of any one period. The period you want to calculate is the amount of time it takes until interest is paid on your deposit -- for example, a day or a month. This is the compounding period. Daily compounding pays interest each day. Monthly compounding pays interest each month and so on.

Periodic Rate

The periodic interest rate is the interest you gain during that period, for example, after a day or after a month. To figure the periodic interest rate for your deposit, divide the yearly nominal rate by the amount of periods within a year. For daily compounding, divide the nominal rate by 365. For monthly compounding, divide the nominal rate by 12 and so on. The periodic rate is also used for loans. Loans are generally paid off with monthly installments. That means that you're always paying one month's worth of interest on the declining balance. The periodic rate for loans is the monthly rate, or the nominal rate divided by 12.

Effective Rate

The effective interest rate is the actual rate of interest you receive over a given time after compounding, or reinvesting, the interest. The formula for converting the periodic rate into the overall effective rate is this: Add 1 to the periodic rate. Raise this number to the power of periods. For two periods, for example, you would raise to the power of two, or square the number. Then subtract one for the rate. For example, if the monthly periodic rate is .005 (half a percent), the effective yearly rate is 1.005 to the 12th power minus 1, which totals a little less than .0617, or 6.17 percent. The nominal yearly rate, on the other hand, is just 6 percent.

Back to the Periodic Rate

You can also change the effective rate back into the periodic rate. Just raise the effective rate plus 1 to the reciprocal power of periods and subtract 1. For example, to convert the yearly effective rate to the monthly rate, first add 1 to the effective rate. Then raise that number to the 1/12th power. Then subtract 1.

Continuous Compounding

The amount of times you can compound is infinite. You can receive interest every second, every half second or every millionth of a second. This infinity reaches a limit at continuous compounding. The formula for the effective rate of continuous compounding is this: multiply any non-compounded rate by the amount of times it shows up overall. You can use the nominal rate itself if you are calculating the yearly effective rate. Call this RT. Raise Euler's number, known as "e," to the power of RT. Subtract 1 for the effective rate. Your deposit times the effective rate is your earnings.

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