Answer to Question #311092 in Financial Math for tumi

Question

The Smart Treasure Fund was created for Samson after he lost his leg in a battle with pirates. The fund has undertaken to pay him R1 200 000 now. Samson prefers to receive three payments: one three years from now; one twice the size of the first payment six years from now, and one four times the size of the first payment ten years from now. The amount of money to the nearest rand that Samson can expect to receive six years from now if the interest rate applicable is 8,6% per year, compounded quarterly, will be

Answer 1

present value = R 1 200 000

lets say he receives R 'X' after 3 years, '2X' after 6 years and 4'X' after 10 years then, present value $=x(1+\frac{8.6}{400})^{-4\times 3}\\=0.77471069$

similarly, for the second payment, $PV_2=1.2003533x \space and\space PV_3 =1.70814665x$

so,$0.77471069x +1.2003533x+1.70814665x=1200000$

solve,

$x=R325802.707809$

so, after 6 years '2X' payment is made,

so, payment made

$=2\times 325802.707809\\=R 651605$