Question

the interest on an investment varies directly as the rate of interest. if the interest is $43 when the interest rate is 5%, find the interest when the rate is 3.7%.

the interest when the rate of interest is 3.7% is $\square$
(simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Define direct variation

Let \( I \) be the interest and \( r \) be the rate. For direct variation, \( I = kr \), where \( k \) is the constant of variation.
We know \( I = 43 \) when \( r = 5\% = 0.05 \). Substitute into the formula:
\( 43 = k\times0.05 \)

Step2: Solve for \( k \)

To find \( k \), divide both sides by \( 0.05 \):
\( k=\frac{43}{0.05}=860 \)

Step3: Find interest at 3.7%

Now, use \( k = 860 \) and \( r = 3.7\%=0.037 \) in \( I = kr \):
\( I = 860\times0.037 \)
\( I = 31.82 \)

Answer:

31.82