Assume an 18 month CD purchased for $7000 pays an APR of 4% compounded monthly. What is the APY?
2 decimal places
I count 9 times that you have posted a variation of the same problem, all you are doing is changing the interest rate.
Here is my first answer when you had it at 3%
http://www.jiskha.com/display.cgi?id=1452909381
It has now been answered by 3 different tutors all using the same method.
ok, how does your text , your course, or your notes define APY ?
To calculate the Annual Percentage Yield (APY) for a 18 month CD, you first need to calculate the Future Value (FV) of the CD after the 18 month period. Here's how you can do it:
Step 1: Convert the APR to a monthly interest rate.
APR stands for Annual Percentage Rate, which is the annual interest rate. To calculate the monthly interest rate, divide the APR by 12 months:
Monthly interest rate = APR / 12 = 4% / 12 = 0.04 / 12 = 0.00333 (round to 5 decimal places)
Step 2: Calculate the Future Value (FV) of the CD.
The Future Value formula for compound interest is:
FV = P(1 + r/n)^(n*t)
where:
FV = Future Value
P = Principal amount (initial investment)
r = Annual interest rate
n = Number of times the interest is compounded per year
t = Number of years
In this case:
P = $7000
r = 0.04 (monthly interest rate)
n = 12 (compounded monthly)
t = 18 months / 12 months = 1.5 years
Using the formula, we can compute the Future Value (FV):
FV = $7000 * (1 + 0.04/12)^(12*1.5)
FV = $7000 * (1.00333)^(18)
FV ≈ $7212.08 (rounded to 2 decimal places)
Step 3: Calculate the APY (Annual Percentage Yield).
The APY formula is given by:
APY = (1 + r/n)^n - 1
In this case:
r = 0.04 (monthly interest rate)
n = 12 (compounded monthly)
Using the formula, we can compute the APY:
APY = (1 + 0.04/12)^12 - 1
APY ≈ 0.040563 (rounded to 6 decimal places)
Converting APY to a percentage:
APY = 0.040563 * 100%
APY ≈ 4.06% (rounded to 2 decimal places)
Therefore, the APY for the 18 month CD with an APR of 4% compounded monthly is approximately 4.06%.