I need help computing the Annual percentage yield (APY) for a savings account that earned $56 in interest on $800 over 365 days?
HELP PLEASE!
To compute the Annual Percentage Yield (APY) for a savings account, you will need to use the formula:
APY = [(1 + r/n)^(n*t)] - 1
Where:
- r is the annual nominal interest rate (expressed as a decimal)
- n is the number of compounding periods per year
- t is the number of years
To calculate the APY, we need to find the nominal interest rate first. We can begin by finding the interest rate for the given amount:
Interest Earned = Principal * Interest Rate * Time
To find the interest rate (r), we can rearrange the formula:
Interest Rate = Interest Earned / (Principal * Time)
For your case, with an interest of $56, a principal (initial deposit) of $800, and a time of 365 days (1 year), we can calculate the interest rate:
Interest Rate = $56 / ($800 * 1) = 0.07
Now, we need to determine the compounding frequency (n). This refers to how often the interest is compounded per year (e.g., annually, semi-annually, quarterly, monthly). Since the question does not specify, we will assume it's compounded annually.
Therefore, n = 1.
Next, we can calculate the APY using the formula mentioned earlier:
APY = [(1 + r/n)^(n*t)] - 1
= [(1 + 0.07/1)^(1*1)] - 1
= [(1 + 0.07)^1] - 1
= (1.07) - 1
= 0.07
So, the Annual Percentage Yield (APY) for this savings account is 0.07 or 7%.