Discounted Value at Simple Interest

Question

Struggling with this question:

Mr. A borrows 2000 now and 3000 in 4 months. He agrees to pay X in 6 months and 2X in 8 months (from now). Determine X using a focal date 8 months from now at simple interest rate r = 12%.

Thanks in advance.

Answer 1

We have the following cash flows \begin{array}{|c|c|c|c|c|} \hline c_t &-2000 & -3000 & x & 2x\\ \hline t & 0 & 4 & 6 & 8\\ \hline \end{array} so at $t=8$ months, putting $i=\frac{12\%}{12}=1\%$ we have $$ -2000(1+i\times 8)-3000(1+i\times 4)+x(1+i\times 2)+2x=0 $$ that is $$ -2160-3120+3.02x=0 $$ and then $$ x=\frac{5280}{3.02}=1748.34 $$

Answer 2

Answer I get is 1,747.47

Essentially you want to find $X$ such that the discounted value of all cash received equals the discounted value of all cash paid. E.g., discounted value today of $100$ at $m$ months time from now at $12$% (p.a.) (simple interest) is $\frac{100}{1+(12\% \times m/12)}$. The rest is a bit of algebra.