Question 12.12: Use the APY formula required by the Truth in Savings Act for...

Use the APY formula required by the Truth in Savings Act for the following calculation. Suppose that a customer holds a savings deposit in a savings bank for a year. The balance in the account stood at $2,000 for 180 days and $100 for the remaining days in the year. If the Savings bank paid this depositor $8.50 in interest earnings for the year, what APY did this customer receive?

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The correct formula is:

 

APY=100[(1+ Interest Earned  Average Account Balance )365/ Daysin Period 1]APY =100\left[\left(1+\frac{\text { Interest Earned }}{\text { Average Account Balance }}\right)^{365 / \text { Daysin Period }}-1\right]

 

In this instance,

 

APY=100[(1+$8.50$1036.99)365/3651]APY =100\left[\left(1+\frac{\$ 8.50}{\$ 1036.99}\right)^{365 / 365}-1\right]

 

Or

 

APY = 0.82 percent,

 

Where the average account balance is:

 

$2000×180 days +$100×185 days 365 days =$1036.99\frac{\$ 2000 \times 180 \text { days }+\$ 100 \times 185 \text { days }}{365 \text { days }}=\$ 1036.99

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