Adebt of $2000 due in five years and $7000 due in seven years is to repaid by a single payment three years from now. if the interest rate is 8% compounded quarterly, how much is the payment?

The single payment three years from now will be of $11,414.17

Step-by-step explanation:

To calculate investments or debts with compound interests you're going to need the following formula:

Where:

V(n) is the value of the debt after n years,

R is the annual interest rate,

t is the number of times the debt is going to be compounded annually,

n is the number of years the debt is going to be compounded,

P is the principal amount being owed.

You know that the debt will be cancelled in 3 years from now. Therefore you have that n = 3 for both debts, because after the 3rd year the debts won't keep compounding interests.

Then you have that t = 4, because the debt is compounded quarterly.

We can add up the two principals $2000 + $7000 = $9000 to make it our value P, so P = 9000.

And finally we have that R = 0.08.

Now you have everything you need to replace in the formula:

Therefore the single payment three years from now is going to be of $11,414.18

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet