# Effective Rate of Interest

• MHB
In summary, a $17,000 T-bill was purchased at a 2.75% discount rate for 20 weeks, which is equal to 5/13 of a year. Using the formula for effective rate of interest, the nominal rate of 0.0275 and compounding periods of 5/13 were used to calculate the effective rate, but further clarification is needed as to whether a discount rate is the same as an interest rate. mathdad A$17,000 T-bill is purchased at a 2.75% discount rate for 20 weeks. Find the effective rate of interest to the nearest hundredth of a percent.

My Effort:

Note: 20 weeks = 20/52 or 5/13 of a year.

Let E = effective rate of interest

E = [1 + (r/m)]^m - 1 where r is the nominal (annual ) advertised rate; m is the number of compounding periods/year.

Let r = 0.0275

Let m = 5/13

1. Is this the correct formula?

2. If so, is my value for r and m correct?

Are you SURE a "Discount" rate is the same as an "Interest" rate? Look up the definitions and make sure.

I'll have to get back to you.

## 1. What is the definition of Effective Rate of Interest?

The Effective Rate of Interest is the actual interest rate that is paid or earned after taking into account compounding interest over a specific period of time.

## 2. How is the Effective Rate of Interest different from the stated interest rate?

The stated interest rate is the percentage that is advertised or agreed upon, while the Effective Rate of Interest takes into account the compounding of interest over time, resulting in a higher or lower actual rate.

## 3. What factors affect the Effective Rate of Interest?

The Effective Rate of Interest is affected by the frequency of compounding, the time period, and the stated interest rate. Higher compounding frequency and longer time periods result in a higher Effective Rate of Interest, while a lower stated interest rate will result in a lower Effective Rate of Interest.

## 4. How is the Effective Rate of Interest calculated?

The Effective Rate of Interest is calculated using the formula: (1 + (r/n))^n - 1, where r is the stated interest rate and n is the number of compounding periods.

## 5. Why is it important to consider the Effective Rate of Interest?

The Effective Rate of Interest gives a more accurate representation of the actual interest rate being paid or earned, allowing for better comparison between different investment or loan options. It also helps individuals and businesses make more informed financial decisions.

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