30. The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie. The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price. The owner has decided to take out a loan to purchase updated equipment. A bank has agreed to loan the owner $2,000 for the purchase of the equipment at a simple interest rate of 4.69% payable annually. To the nearest dollar, what is the total amount the shop owner will pay on the loan over the 3 years?
Answer: B
The total amount the shop owner will pay on the loan over the 3 years is $2,276.
To calculate the total amount payable on the loan over 3 years, we can use the simple interest formula: Total Amount = Principal + (Principal × Rate × Time). In this case, the principal is $2,000, the interest rate is 4.69%, and the time is 3 years. This results in a total payment of $2,276.
A) $2,028
This option is incorrect because it does not accurately reflect the total amount payable based on the loan's interest calculation. The amount calculated using the simple interest formula would yield a higher total than this figure.
B) $2,276
This option is correct as it properly accounts for the principal of $2,000 and the accrued interest over 3 years at a simple interest rate of 4.69%. The calculation shows that the total amount paid back will indeed be $2,276.
C) $2,760
This option is incorrect as it significantly overestimates the total payment due. The calculation of simple interest does not support such a high total, indicating a misunderstanding of the loan's terms or calculation method.
D) $2,092
This option is incorrect as it underestimates the total amount payable on the loan. The calculation based on the simple interest rate indicates a higher total payment than this amount.
Conclusion
The correct answer, $2,276, results from a precise calculation of the loan's simple interest over 3 years, confirming that this option accurately reflects the financial obligation of the shop owner. All other options fail to correctly apply the simple interest formula, resulting in either an underestimation or overestimation of the total payment.