Final answer:
Using the direct variation formula y = kx, the constant of variation (k) is first found to be $960 using the given interest of $48 at a rate of 5%. To find the interest at a rate of 9.4%, we multiply k by 9.4% to get an interest of $90.24.
Step-by-step explanation:
To solve the variation problem stated where the interest on an investment varies directly as the rate of interest, we will use the concept of direct variation. The formula for direct variation is y = kx, where y represents the interest amount, k is the constant of variation, and x is the rate of interest.
First, we calculate the constant of variation (k) using the information given:
Interest ($48) = k × Rate (5%), or
$48 = k × 0.05
Solving for k gives us:
k = $48 / 0.05 = $960.
Now, to find the interest when the rate is 9.4%, we substitute the known values into the direct variation formula:
Interest = k × Rate (9.4%), or:
Interest = $960 × 9.4% = $960 × 0.094.
Thus, the interest when the rate is 9.4% is:
Interest = $960 × 0.094 = $90.24.
The interest at a 9.4% rate would be $90.24.