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Chapter 5: Problem 24

Find the effective rate corresponding to the given nominal rate. \(8 \% /\) year compounded daily

Short Answer

Expert verified
The effective annual rate corresponding to the given nominal rate of \(8\%\) compounded daily is approximately \(8.3\%\).

Step by step solution

01

Identify the given information

We are given: - Nominal rate (r) = \(8\%\) - Compounding periods in a year (n) = daily (compounded daily)
02

Convert the nominal rate to a decimal

To convert the percentage to a decimal number, divide the percentage by 100: Nominal rate (r) = \(8\% = \frac{8}{100} = 0.08\)
03

Find the number of compounding periods in a year

Since the interest is being compounded daily, there are 365 compounding periods in a year (ignoring leap years). We denote this as: n = 365
04

Apply the formula for the effective annual rate

The formula for calculating the effective annual rate (EAR) when given a nominal rate and the number of compounding periods is: \[EAR = (1 + \frac{r}{n})^n - 1\] We have r = 0.08 and n = 365, so: \[EAR = (1 + \frac{0.08}{365})^{365} - 1\]
05

Evaluate the expression

Now, we will calculate the value of EAR: \[EAR = (1 + \frac{0.08}{365})^{365} - 1 \approx 0.083 \] The result is given in a decimal form. To convert it back to a percentage, we multiply by 100: \[EAR = 0.083 \times 100 = 8.3\%\]
06

State the answer

The effective annual rate corresponding to the given nominal rate of \(8\%\) compounded daily is approximately \(8.3\%\).

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Most popular questions from this chapter

Jodie invested \(\$ 15,000\) in a mutual fund 4 yr ago. If the fund grew at the rate of \(9.8 \%\) lyear compounded monthly, what would Jodie's account be worth today?

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