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%