Determine the effective annual yield (annual percentage yield) for $1
invested for 1 year at 8.5% compounded monthly.
let that rate be i
(1+i)^1 = (1+.085/12)^12
1+i = 1.08839
i = .08839
so the effective annual rate is 8.839%
Thanks a lot
To determine the effective annual yield, we need to calculate the annual percentage yield (APY) for the given interest rate compounded monthly.
Step 1: Convert the interest rate to a decimal form.
The interest rate is 8.5%, so we divide it by 100 to convert it to decimal form: 8.5% / 100 = 0.085.
Step 2: Calculate the monthly interest rate.
Since the interest is compounded monthly, we need to divide the annual interest rate by 12 (the number of months in a year): 0.085 / 12 = 0.00708333.
Step 3: Calculate the effective annual yield (APY) using the formula:
APY = (1 + Monthly interest rate)^12 - 1.
Substituting the values:
APY = (1 + 0.00708333)^12 - 1.
Using a calculator, we can evaluate this expression:
APY = (1.00708333)^12 - 1 = 0.0937946.
Step 4: Convert the APY to a percentage form.
Multiply the APY by 100 to express it as a percentage: 0.0937946 * 100 = 9.37946.
So, the effective annual yield (annual percentage yield) for $1 invested for 1 year at 8.5% compounded monthly is approximately 9.38%.
To determine the effective annual yield (annual percentage yield), you need to consider the compounding frequency. In this case, the investment is compounded monthly, which means that interest is added to the investment balance every month.
The formula for effective annual yield (EAY) is as follows:
EAY = (1 + r/n)^n - 1
Where:
- r is the nominal interest rate (in decimal form)
- n is the number of compounding periods in one year (in this case, 12 months)
In this example, the nominal interest rate is 8.5% per year, compounded monthly. Therefore, we need to convert the interest rate to a decimal by dividing it by 100:
r = 8.5% / 100 = 0.085
The number of compounding periods in one year is 12 since interest is compounded monthly.
Now, we can calculate the effective annual yield (EAY) using the formula:
EAY = (1 + 0.085/12)^12 - 1
Let's solve the equation:
EAY = (1 + (0.085/12))^12 - 1
Calculating the intermediate step:
(0.085/12) ≈ 0.007083333
EAY = (1 + 0.007083333)^12 - 1
Calculating the exponent:
(1 + 0.007083333)^12 ≈ 1.087898685
EAY = 1.087898685 - 1
Calculating the difference:
1.087898685 - 1 ≈ 0.087898685
Therefore, the effective annual yield for $1 invested for 1 year at 8.5% compounded monthly is approximately 0.0879, or 8.79%.