Answer:
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:
[tex]V(n)= (1+\frac{R}{t})^{tn}*P[/tex]
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:
[tex]V(3)= (1+\frac{0.08}{4})^{4*3}*9000=11414.18[/tex]
Therefore the single payment three years from now is going to be of $11,414.18
