Question

The interest on an investment varies directly as the rate of interest. If the interest is ​$41 when the interest rate is 4​%, find the interest when the rate is 7%.

Answer 1

First, find what 41 is 4% of.

`(4)/(100) = (41)/(x)`

`4x = 4100`

`x = 1025`
Now find 7% of 1025.

`1025(.07) = 71.75`
The interest would be $71.75

Answer 2

$ 71.75

Explanation:

Suppose r represents the interest rate and I represents the amount of interest,

∵ the interest on an investment varies directly as the rate of interest,

i.e. I ∝ r

⇒ I = kr

Where,

k = constant of variation,

If I = 41, r = 4% = 0.04,

`\implies 41=0.04k\implies k = (41)/(0.04)=1025`

Thus, the equation that shows the relation between I and r is,

I = 1025 r

If r = 7% = 0.07,

Thus, the interest would be,

I = 1025 × 0.07 = $ 71.75