If you deposit money in a savings account with an interest rate (APR) of 5% and the account compounds quarterly, which is your annual percentage yield (APY)? Convert your answer to a percent and round it to two decimal places.
P = Po(1+r)^n.
We can use any value for the Initial
deposit, but the for the time should be
for one year.
Po = $1.00.
r = (5%/4)/100% = 0.0125 = Quarterly %
rate expressed as a decimal.
n = 4comp./yr * 1yr = 4 Compounding periods.
P = (1.00(1.0125)^4 = $1.0509.
APY = ((P-Po)/Po) * !00%.
APY=((1.0509-1.00)/1.00) * 100%=5.09%.
To calculate the Annual Percentage Yield (APY) for a savings account, you need to take into account the interest rate (APR) and the compounding frequency.
First, convert the APR from a yearly rate to a quarterly rate by dividing it by 4. In this case, the APR is 5%, so the quarterly interest rate would be 5 / 4 = 1.25%.
Next, calculate the APY by using the formula: APY = (1 + r/n)^n - 1, where:
- r is the quarterly interest rate as a decimal (1.25% = 0.0125),
- n is the number of compounding periods per year (4 for quarterly compounding).
Plugging in the values:
APY = (1 + 0.0125/4)^4 - 1
APY = (1.003125)^4 - 1
APY ≈ 1.012536 - 1
APY ≈ 0.012536 = 1.2536%
Therefore, the annual percentage yield (APY) for the savings account with a 5% APR and quarterly compounding is approximately 1.25% when rounded to two decimal places.
To calculate the annual percentage yield (APY) for a savings account that compounds quarterly, you can use the formula:
APY = (1 + (APR / n))^n - 1
Where:
- APR is the annual interest rate (in decimal form)
- n is the number of compounding periods in a year (in this case, 4 for quarterly compounding)
In this case, the APR is 5% or 0.05 in decimal form.
APY = (1 + (0.05 / 4))^4 - 1
Simplifying the equation:
APY = (1.0125)^4 - 1
Calculating the result:
APY = 1.051010126 - 1
APY = 0.051010126
Converting the result to a percentage and rounding to two decimal places:
APY ≈ 5.10%
Therefore, the annual percentage yield (APY) for the savings account is approximately 5.10%.