Assume an 18-month CD purchased for $7000 pays an APR of 3% compounded monthly. What is the APY?
I will assume APY means the effective annual interest rate.
let that rate be i
(1+i)^1 = (1 + .03/12)^12
1+i = 1.030416
i = .030416 = 3.0416%
Well, did you know that in the world of finance, there's a lot of confusing acronyms? APR, APY, ABC... it's like they're trying to create their own secret language! Anyway, let me break it down for you.
APR stands for Annual Percentage Rate, which tells you how much interest you'll earn in a year. In this case, it's 3%.
APY, on the other hand, stands for Annual Percentage Yield. It takes into consideration the compounding frequency of the interest. Since the CD compounds monthly, the APY will be slightly higher than the APR.
Now, let's crunch some numbers and find that APY! With an APR of 3% compounded monthly, I'd say the APY would be around... tada! 3.04%!
So remember, in finance, they may have invented acronyms to confuse us, but with a little bit of math and a sprinkle of humor, we can figure it all out!
To calculate the APY (Annual Percentage Yield), we need to understand how it is different from the APR (Annual Percentage Rate).
The APR represents the nominal interest rate on an investment, while the APY reflects the true effective annual interest rate, taking into account the effects of compounding.
To find the APY, we can use the following formula:
APY = (1 + (APR/n))^n - 1
APR represents the annual interest rate, and "n" represents the number of compounding periods per year (in this case, 12 since it's compounded monthly).
Given that the APR is 3%, we can plug these values into the formula to calculate the APY.
APY = (1 + (0.03/12))^12 - 1
Simplifying:
APY = (1.0025)^12 - 1
Using a calculator, we find:
APY = 0.030428
Therefore, the APY is approximately 3.04%.
To determine the APY (Annual Percentage Yield), we can use the formula:
APY = (1 + r/n)^n - 1
Where:
- r is the annual interest rate (APR) expressed as a decimal
- n is the number of compounding periods per year
In this case, the APR is 3% (0.03) and the compounding occurs monthly (n = 12).
First, let's calculate the monthly interest rate (r/n):
r/n = 0.03 / 12 = 0.0025
Next, we can calculate (1 + r/n)^n:
(1 + 0.0025)^12
Calculating this expression will give us the factor by which the initial amount will grow over the year.
So, here's how you can solve this with a calculator:
1. Add 1 to the monthly interest rate: 1 + 0.0025 = 1.0025
2. Raise this number to the power of 12: (1.0025)^12
3. Subtract 1: (1.0025)^12 - 1 = 0.03036 (rounded to 5 decimal places)
The result, 0.03036, represents a growth of 3.036% over the course of a year. Therefore, the Annual Percentage Yield (APY) is 3.036%.