Answer to Question #169892 in Financial Math for JC

Question

A motor bike was originally listed at $769.99. The price was first discounted to $550.54, followed by a final discounted price of $449.79. What was the single equivalent rate of discount at the final price? (leave answer to 2 decimal places)

Answer 1

The single equivalent rate of discount $= 1 -[(1-d_1)(1-d_2)]$

Proportion:

769.99 – 100 %

550.54 – $P_2$

$P_2 = \frac{550.54 \times 100}{769.99} = 71.4999 \\ d_1 = 100 -71.499 = 28.50 \%$

Proportion:

550.54 – 100%

449.79 – $P_3$

$P_3 = \frac{449.79 \times 100}{550.54} = 81.6997 \\ d_2 = 100 -81.6997 =18.30 \%$

The single equivalent rate of discount = 1 -[(1-0.2850)(1-0.1830)]

$= 1 -[0.715 \times 0.817] \\ = 0.4158$

The single equivalent rate of discount is 41.58 %.