Answer to Question #194165 in Financial Math for Zethembiso

Question

Fisokuhle has a textbook loan that was supposed to be paid in two payments of R1637 due six months ago and R1746 due in nine months from now. Instead he renegotiate to pay R622 today and the balance in three months, therefore the settlement is at month three. The debts and payments are subject to the same interest rate of 9% per annum compounded quarterly. Represented in a timeline what is the value of X (month three)

Answer 1

According to question-

$\Rightarrow 3(x-2)-4-4 \\ \Rightarrow 3x-6-4x=-4 \\ \Rightarrow -x-6=-4 \\ \Rightarrow x=-2$

i=9%=0.09

n=4( quarterly compounded)

Thus value of x is equal to the sum of value at time 3-

$x=1637(1+\dfrac{0.09}{4})^3+1746(1+\dfrac{0.09}{4})^{2}-622(1+\dfrac{0.09}{4})^1$

$x=R1750+R1670-R636\\[9pt] x=R2784$

Hence The value of x is R2784.