Determine the constant of variation for the stated condition.
-The amount of simple interest earned on an investment over a fixed amount of time is jointly proportional to the principle invested and the interest rate. A principle investment of $2000.00 with an interest rate of 1% earned $100.00 in simple interest. Find the amount of simple interest earned if the principle is $3500.00 and the interest rate is 8%.
A) $1400.00
B) $140,000.00
C) $175.00
D) $800.00

Question

Quizplus · Accepted Answer

The constant of variation (k) can be found using the formula for simple interest: I = PRT, where I is the interest earned, P is the principal, R is the rate, and T is the time. Given that T is constant and not provided, we can assume it to be part of the constant of variation. From the given information, $100 = $2000 * 1% * k, solving for k gives us k = 1 (since 1% is 0.01, and 100 = 2000 * 0.01 * k). For a principal of $3500 and a rate of 8%, the interest earned would be I = $3500 * 8% * 1 = $280. However, the correct calculation should be based on the formula without assuming k because the time factor is implicitly considered constant. The correct calculation is I = PRT without needing to solve for k, which was incorrectly approached in the explanation. The correct interest for $3500 at 8% is actually $280, indicating a mistake in the initial calculation and choice selection. The correct approach to find the interest without the unnecessary step of finding k would directly apply the given formula: I = PRT, leading to the realization that none of the provided options match the correct calculation of $280, suggesting a reevaluation of the answer choices or an error in the question's setup or answer options.

Determine the Constant of Variation for the Stated Condition