by Susan Ow

Created on: January 04, 2009

Most people have encountered such situations in practice. For example, Bank A charges an annual effective rate of 8% on loans, while Bank B charges 8% compounded monthly. Most people probably realize that these rates are not directly comparable, but they probably not able to make a distinction between Bank A's rate and Bank B's rate.

Bank A is charging an annual effective interest rate, and Bank B is charging a nominal rate of interest.

The nominal interest rate is an interest rate without the adjustment of the full effect of compounding; For example, an annual nominal interest rate of 8% compounding quarterly does not mean an interest rate of 8% per quarter, but rather an interest rate of 2% per quarter.

The effective interest rate is the amount of money will earn during the period for one unit of money invests at the beginning of a period, given that interest is paid at the end of the period. For example, an annual effective rate of 8% means that you will receive $0.08 with a dollar invested at the beginning of the year. If the interest rate is quoted as quarter effective rate of 8%, you will receive $0.08 at the end of quarter instead of at the end of the year.

Nominal interest rate is used when interest is paid more frequently than once per period, whereas effective interest rate is used to convert the nominal interest rate to annual rate. The effective interest rate is calculated in the following way:

r = (1 + i/n)^n

where r is effective interest rate, i is nominal interest rate, and n is frequency payment per year.

For example, a nominal interest rate of 12% compounded monthly is equivalent to an effective interest rate of 12.68%. Every month, 1% interest is credited into the account. After one year, the total amount is (1+0.01)^12 = 1.1268 with $1 invested at the beginning of the year.

If the nominal interest rate is compounded continuously, the calculation will be:

r = exp(i) - 1

where r is effective interest rate, I is nominal interest rate, and exp(i) is exponential function of i.

When looking at nominal interest rate, pay attention to the following terms: compounding semiannually, quarterly, monthly, daily, or continuously. With $1 dollar invested at the beginning of the year, the effective interest rates for a nominal interest rate of 12% compounded semiannually, quarterly, monthly, daily, and continuously are 12.36%, 12.55%, 12.68%, 12.75% and 12.75%.

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