Assume an 18-month CD purchased for $7000 pays an APR of 5% compounded monthly. What is the APY?
APY=____%
To calculate the APY (Annual Percentage Yield), we need to take into account the effects of compounding over a year. The formula to calculate APY is:
APY = (1 + (APR / n))^n - 1
Where APR is the Annual Percentage Rate and n is the number of compounding periods per year.
In this case, the APR is 5% and the compounding is monthly, so n is 12 (since there are 12 months in a year).
Using the formula, we can calculate the APY:
APY = (1 + (0.05 / 12))^12 - 1
Simplifying the equation:
APY = (1.0041667)^12 - 1
APY = 1.051161898 - 1
APY = 0.051161898
To express this as a percentage, we multiply by 100:
APY = 0.051161898 * 100
APY = 5.1161898%
Therefore, the APY is approximately 5.12%.
To find the APY (Annual Percentage Yield), we need to use the formula:
APY = (1 + r/n)^n - 1
Where:
r is the nominal interest rate (APR)
n is the number of compounding periods per year
In this case, the APR is 5% and the compounding is done monthly, so the compounding period is 12 (since there are 12 months in a year).
Let's calculate the APY:
1. Convert the APR to the decimal form:
APR = 5% = 5/100 = 0.05
2. Plug the values into the formula:
APY = (1 + 0.05/12)^12 - 1
Now, let's calculate it:
APY = (1 + 0.05/12)^12 - 1
= (1 + 0.0041667)^12 - 1
≈ 0.0511618987
To express the APY as a percentage, multiply by 100:
APY ≈ 0.0511618987 * 100
≈ 5.11618987%
Therefore, the APY is approximately 5.12%.
P=Po(1+r)^n. Calculate int. for 1 year.
r = (5%/12)/100% = 0.00417 = Monthly %
rate expressed as a decimal.
n = 12comp./yr. * 1yr. = 12 Compounding
periods.
P = 7000(1.00417)^12 = $7358.13
I = P-Po = 7358.13 - 7000 = $358.13
APY = (I/Po)*100% = (358.13/7000)*100% = 5.116%