Question

A debt 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?

Answer 1

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

Explanation:

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

`V(n)= (1+(R)/(t))^(tn)*P`

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:

`V(3)= (1+(0.08)/(4))^(4*3)*9000=11414.18`

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