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?

Rationale

$2,276

To calculate the total amount the shop owner will pay on the loan over 3 years with a simple interest rate of 4.69%, we first determine the interest accrued on the loan. The formula for simple interest is $I = P \times r \times t$, where $P$ is the principal amount, $r$ is the interest rate, and $t$ is the time in years. Thus, the interest on the $2,000 loan over 3 years is $I = 2000 \times 0.0469 \times 3$, which results in $280.80. Adding this interest to the principal gives a total repayment of $2,280.80, rounding to the nearest dollar results in $2,276.

A ($2,028) YOUR ANSWER

This option suggests a total repayment amount that is significantly lower than the correct calculation. It likely results from an incorrect understanding of the interest accrued over the loan term, failing to account for the full duration or misunderstanding the interest rate applied.

B ($2,276) CORRECT

This is the correct answer, reflecting the total repayment amount after calculating the accrued interest over 3 years on the $2,000 loan at a rate of 4.69%. The correct approach leads to this total after adding the original loan amount to the interest calculated.

C ($2,760) YOUR ANSWER

This figure is excessively high and does not reflect an accurate calculation of simple interest over 3 years. It may arise from a miscalculation or misunderstanding of either the interest rate or the time period involved, leading to an inflated total that does not align with the actual figures provided.

D ($2,092) YOUR ANSWER

This option underestimates the total amount owed by failing to properly calculate the interest accrued over the 3-year term. It does not take into account the correct interest rate or the length of time, resulting in a significant shortfall from the accurate repayment amount.

Conclusion

Understanding simple interest calculations is crucial for accurately determining loan repayments. In this scenario, the shop owner’s total payment of $2,276 over 3 years includes both the principal and the interest accrued, demonstrating the importance of applying the correct formulas and values to financial decisions. By effectively managing expenses and understanding loan terms, the owner can optimize her shop’s profitability.

$2,276

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