Save \& Exit Certify Lesson: 6.1 Understanding Interest 5/14 Question 9 of 14, Step 1 of 1 Correct Milo is purchasing a new refrigerator for \( \$ 1300 \) using an in-store offer. The store is offering a 30 days same-as-cash loan. This means that at the end of the 30 days, if Milo has paid off the cost of the refrigerator, he owes no added interest charge, but if he does not pay off the entire cost of the refrigerator, he owes simple interest on the original purchase amount, calculated over the entire 30 days. If the annual interest rate is \( 24.13 \% \), how much would Milo owe on the \( 31^{\text {st }} \) day if he made no payments during the first 30 days? Round your answer to the nearest cent, if necessary. Formulas Simple Interest Future Value for Simple Interest Future Value for Compound Interest Future Value for Continuous Compound Interest \[ \begin{array}{l} I=P r t \\ A=P(1+r t) \\ A=P\left(1+\frac{r}{n}\right)^{n t} \\ A=P e^{n t} \end{array} \] Annual Percentage Yield (APY) \[ \mathrm{APY}=\left(1+\frac{r}{n}\right)^{n}-1 \]
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To find the total amount Milo owes after 30 days, we need to calculate the simple interest based on the formula \( I = P \times r \times t \). Here, \( P \) is the principal amount (\$1300), \( r \) is the annual interest rate (0.2413), and \( t \) is the time in years (30 days is \( \frac{30}{365} \)). Plugging in the values: \[ I = 1300 \times 0.2413 \times \frac{30}{365} \approx 32.05. \] So on the \( 31^{st} \) day, if Milo hasn't made any payments, he will owe the original amount plus the interest, which totals approximately \( \$ 1332.05 \). While loans with "same-as-cash" offers can seem appealing, it's important to be mindful of what happens if you miss the deadline. Many consumers assume they'll easily make the payment but find themselves strapped for cash at the last minute. Always consider your ability to pay off the loan in the given time to avoid those gnarly interest charges at the end! Planning ahead is key to staying debt-free.
