QuestionMay 27, 2025

Rosie borrows 17,500 to buy a used car and the car dealer offers a 9.3% simple interest car loan. She wants to keep her payments at 375 per month. What term should her loan be (find the least amount of months that will make her payment under her budget)? square months

Rosie borrows 17,500 to buy a used car and the car dealer offers a 9.3% simple interest car loan. She wants to keep her payments at 375 per month. What term should her loan be (find the least amount of months that will make her payment under her budget)? square months
Rosie borrows 17,500 to buy a used car and the car dealer offers a 9.3% simple interest car loan. She wants to keep her payments at 375 per month. What term should her loan be (find the least amount of months that will make her payment under her budget)? square months

Solution
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Answer

82 months Explanation 1. Calculate Total Interest Use the formula for simple interest: I = P \cdot r \cdot t, where P = 17500, r = 0.093. We need to find t such that monthly payments are \leq 375. 2. Calculate Monthly Payment Total amount to be paid is A = P + I. Monthly payment is M = \frac{A}{t}, and we want M \leq 375. 3. Set Up Inequality Substitute I = 17500 \cdot 0.093 \cdot t into A = 17500 + I. Then solve \frac{17500 + 17500 \cdot 0.093 \cdot t}{t} \leq 375. 4. Solve for t Simplify inequality: 17500 + 1627.5t \leq 375t. Rearrange: 375t - 1627.5t \geq 17500. Solve: 212.5t \geq 17500. Thus, t \geq \frac{17500}{212.5}.

Explanation

1. Calculate Total Interest<br /> Use the formula for simple interest: $I = P \cdot r \cdot t$, where $P = 17500$, $r = 0.093$. We need to find $t$ such that monthly payments are $\leq 375$.<br />2. Calculate Monthly Payment<br /> Total amount to be paid is $A = P + I$. Monthly payment is $M = \frac{A}{t}$, and we want $M \leq 375$.<br />3. Set Up Inequality<br /> Substitute $I = 17500 \cdot 0.093 \cdot t$ into $A = 17500 + I$. Then solve $\frac{17500 + 17500 \cdot 0.093 \cdot t}{t} \leq 375$.<br />4. Solve for $t$<br /> Simplify inequality: $17500 + 1627.5t \leq 375t$. Rearrange: $375t - 1627.5t \geq 17500$. Solve: $212.5t \geq 17500$. Thus, $t \geq \frac{17500}{212.5}$.
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