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.
(1+.0375/365)^365 = 1.0382, or 3.82%
To find the effective annual yield, we first need to understand what it means. The effective annual yield represents the total amount of interest earned in one year, taking into account the compounding frequency.
In this case, the interest is compounded daily, which means that the interest is calculated and added to the account balance every day. To calculate the effective annual yield, we can use the formula:
Effective Annual Yield = (1 + (interest rate / compounding frequency)) ^ compounding frequency - 1
Let's calculate it step by step:
1. Convert the interest rate to decimal form: 3.75% = 0.0375.
2. Calculate the daily interest rate: 0.0375 / 365 = 0.0001027397 (rounded to 10 decimal places).
3. Substitute the values into the formula:
Effective Annual Yield = (1 + 0.0001027397) ^ 365 - 1
4. Calculate the result:
Effective Annual Yield = 1.040929 - 1 = 0.040929 (rounded to 6 decimal places).
5. Convert the result to a percentage:
Effective Annual Yield = 0.040929 * 100 = 4.09% (rounded to the nearest hundredth of a percent).
Therefore, the effective annual yield for an account with a $3700 investment at a 3.75% interest rate compounded daily is approximately 4.09%.