For a given interest​ rate, simple interest varies jointly as the principal and time. If ​$2000 left in an account for 6 years earned interest of ​$960, then how much interest would be earned in 7 ​years?

i = kpt, so if p is the same,

i/t = pk is constant.
Thus, you want i such that

960/6 = i/7

That is, since 7 is 7/6 as big as 6, the interest will be 7/6 * 960

To solve this problem, we can use the formula for simple interest:

Simple Interest = Principal x Rate x Time

Given that $2000 left in an account for 6 years earned interest of $960, we can substitute these values into the formula and solve for the rate.

$960 = $2000 x Rate x 6

Dividing both sides of the equation by ($2000 x 6), we get:

Rate = $960 / ($2000 x 6) = 0.08

Now that we have the rate, we can calculate the interest earned in 7 years using the same formula:

Interest = Principal x Rate x Time

Interest = $2000 x 0.08 x 7 = $1120

Therefore, the interest earned in 7 years would be $1120.

To solve this problem, we need to use the formula for simple interest, which is given by:

I = P * r * t,

where:
I is the interest earned,
P is the principal amount,
r is the interest rate, and
t is the time period.

In this case, we are given that the principal, P, is $2000 and the time period, t, is 6 years. We are also given that the interest, I, is $960. We need to find the interest earned in 7 years.

Let's calculate the interest rate, r, first. We can rearrange the formula and solve for r:

r = I / (P * t) = $960 / ($2000 * 6) = 0.08.

So, the interest rate is 0.08 or 8%.

Now, we can plug the values of P, r, and t into the formula to find the interest earned in 7 years:

I = P * r * t = $2000 * 0.08 * 7 = $1120.

Therefore, the interest earned in 7 years would be $1120.