Interest rates are often expressed in different ways, such as nominal, effective, periodic, or annual. To compare different interest rates or perform calculations, you may need to convert them from one form to another. Excel provides several functions and formulas that can help you with this task.
The interest rate is the percentage of the principal amount that is paid or received over a certain period of time. The interest rate can be compounded, meaning that the interest is added to the principal and then earns interest itself, or simple, meaning that the interest is calculated only on the initial principal.
The nominal interest rate is the annual interest rate that does not account for compounding. The effective interest rate is the annual interest rate that accounts for compounding. The periodic interest rate is the interest rate per payment period, such as month, quarter, or year. The annual interest rate is the interest rate per year, which can be either nominal or effective.
To convert between different interest rates, you need to know the number of compounding periods per year, which is also called the frequency. For example, if the interest is compounded monthly, the frequency is 12. If the interest is compounded quarterly, the frequency is 4.
Procedures
To convert interest rates in Excel, you can use the following functions and formulas:
- To convert a nominal interest rate to an effective interest rate, use the EFFECT function:
=EFFECT(nominal_rate, frequency)where
nominal_rateis the nominal interest rate per year andfrequencyis the number of compounding periods per year. - To convert an effective interest rate to a nominal interest rate, use the NOMINAL function:
=NOMINAL(effective_rate, frequency)where
effective_rateis the effective interest rate per year andfrequencyis the number of compounding periods per year. - To convert a periodic interest rate to an annual interest rate, multiply the periodic interest rate by the frequency:
=periodic_rate * frequencywhere
periodic_rateis the interest rate per payment period andfrequencyis the number of payment periods per year. - To convert an annual interest rate to a periodic interest rate, divide the annual interest rate by the frequency:
=annual_rate / frequencywhere
annual_rateis the interest rate per year andfrequencyis the number of payment periods per year.
Example
To illustrate how to convert interest rates in Excel, let’s consider the following scenario:
You have a loan of $10,000 with a nominal interest rate of 12% per year, compounded monthly. You want to know the effective interest rate, the monthly interest rate, and the total interest you will pay over one year.
To find the effective interest rate, use the EFFECT function:
`=EFFECT(0.12, 12)`
The result is 0.1268, or 12.68%.
To find the monthly interest rate, use the formula:
`=0.12 / 12`
The result is 0.01, or 1%.
To find the total interest, use the FV function:
`=FV(0.01, 12, -10000, 0) - 10000`
where 0.01 is the monthly interest rate, 12 is the number of payments, -10000 is the present value of the loan, and 0 is the future value of the loan. The result is 1268.24, which is the interest amount.
You can also use an Excel table to show the calculations, as shown below:
| Nominal Rate | Frequency | Effective Rate | Periodic Rate | Total Interest |
|---|---|---|---|---|
| 12% | 12 | 12.68% | 1% | $1,268.24 |
Other Approaches
There are other ways to convert interest rates in Excel, such as using the RATE function or the IRR function. However, these functions require more inputs and may not always converge to a solution. Therefore, the functions and formulas described above are simpler and more reliable for most cases.
