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Chapter 8: Problem 53

You invest \(\$ 1600\) in an account paying \(5.4 \%\) interest compounded daily. What is the account's effective annual yield? Round to the nearest hundredth of a percent.

Short Answer

Expert verified
The account's effective annual yield, when rounded to the nearest hundredth of a percent, is 5.56\%.

Step by step solution

01

Convert Percentage Interest Rate to Decimal Form

The given annual interest rate is 5.4 percent. Convert the percentage to decimal by dividing by 100: \(r = \frac{5.4}{100} = 0.054\).
02

Identify the Number of Compounding Periods

Because the interest is compounded daily, there are 365 compounding periods in a year: \(n = 365\). The time 't' for annual yield is 1 year: \(t = 1\).
03

Calculate the Effective Annual Yield

Use the APY formula to calculate the result: \(APY = (1 + \frac{r}{n})^{(n \cdot t)} -1 = (1 + \frac{0.054}{365})^{(1 \cdot 365)} -1\). Edward, use a calculator for this step as this number will be a tiny decimal that needs to be round up to the nearest hundredth of a percent.
04

Convert APY to Percentage Form

To convert the decimal APY back to percentage form, multiply by 100.

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Most popular questions from this chapter

Make Sense? In Exercises 47-53, determine whether each statement makes sense or does not make sense, and explain your reasoning. By putting \(\$ 10\) at the end of each month into an annuity that pays \(3.5 \%\) compounded monthly, I'll be able to retire comfortably in just 30 years.

In Exercises 11-18, a. Determine the periodic deposit. Round up to the nearest dollar. b. How much of the financial goal comes from deposits and how much comes from interest?$$ \begin{array}{|l|l|l|l|} \hline \$ ? \text { at the end of each month } & 4.5 \% \text { compounded monthly } & 10 \text { years } & \$ 200,000 \\ \hline \end{array} $$

Describe the difference between a fixed installment loan and an open-end installment loan.

Suppose that at age 25 , you decide to save for retirement by depositing \(\$ 50\) at the end of each month in an IRA that pays \(5.5 \%\) compounded monthly. a. How much will you have from the IRA when you retire at age 65 ? b. Find the interest.

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