Will has money invested in a savings account earning 5% compounded daily. What is the effective interest rate?
To calculate the effective interest rate, we need to know the annual interest rate and the frequency with which it is compounded. In this case, we have the information that Will's savings account earns 5% interest compounded daily.
Step 1: Convert the annual interest rate to a decimal.
The annual interest rate is given as 5%. To convert it to a decimal, divide it by 100:
5% / 100 = 0.05
Step 2: Determine the number of compounding periods in a year.
In this case, the interest is compounded daily. Since there are 365 days in a year, the number of compounding periods per year is 365.
Step 3: Use the formula to calculate the effective interest rate.
The formula to calculate the effective interest rate is:
Effective Interest Rate = (1 + (annual interest rate / number of compounding periods))^(number of compounding periods) - 1
Substituting the values we have:
Effective Interest Rate = (1 + (0.05 / 365))^(365) - 1
Now, let's calculate:
Effective Interest Rate = (1 + (0.05 / 365))^(365) - 1
Effective Interest Rate = (1 + 0.0001369863)^(365) - 1
Effective Interest Rate = (1.0001369863)^(365) - 1
Effective Interest Rate ≈ 0.051161897 - 1
Effective Interest Rate ≈ 0.051161897 ≈ 5.1161897%
Therefore, the effective interest rate for Will's savings account is approximately 5.1161897%.