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Chapter 8: Problem 54

You invest \(\$ 3700\) in an account paying \(3.75 \%\) interest compounded daily. What is the account's effective annual yield? Round to the nearest hundredth of a percent.

Short Answer

Expert verified
The effective annual yield is approximately 3.82%.

Step by step solution

01

Understanding the Variables

Let's identify the variables needed. The principal amount (P) invested is $3700, the interest rate (r) is 3.75% and since it is compounded daily, the number of times interest is compounded in a year (n) is 365.
02

Convert the Interest Rate

Convert the annual interest rate from a percentage to a decimal by dividing it by 100, i.e., \(r = 3.75 / 100 = 0.0375\).
03

Calculate Effective Annual Yield

The annual yield (A) can be calculated as \(A = (1 + r/n)^(nt) - 1\). For this problem since we want to know the annual yield, t = 1. Therefore, substituting the values into the formula we get \( A = (1 + 0.0375/365)^(365*1) - 1 \).
04

Calculate and Round the Result

Calculate this expression to get the exact annual yield. Then, multiply this result by 100 to get the percentage and round to two decimal places as we want to get the nearest hundredth of a percent.

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