How to do this discount question

[Simon T]

The star camera center ordered a special lens from one of their suppliers. This lens is listed at 600 dollars with trade discounts of 20% and 5%. An invoice dated November 14 with terms 8/10, 4/20, n/30 EOM was enclosed with the lens when it was delivered to the Star Camera Centre on November 17. Determine for the Star Camera Centre the size of the partial payment they must make to their supplier on December 10 in order to reduce the unpaid balance to 200 dollars.

how do you do this question? This is what I have so far:

CP = 600 (1-8)(1-20)(1-5)
CP = 600 (0.92)(0.8)(0.95)
CP = 600 (0.6992)
CP = 419.52

 

[soroban]

The Star Camera Center ordered a special lens from one of their suppliers.
This lens is listed at \$600 with trade discounts of 20% and 5%.
An invoice dated November 14 with terms 8/10, 4/20, n/30 EOM was enclosed with the lens
when it was delivered to the Star Camera Centre on November 17.
Determine for the Star Camera Centre the size of the partial payment they must make
to their supplier on December 10 in order to reduce the unpaid balance to \$200.

The trade discounts means the Camera Center owes:
. . $$\$600 \times 80\% \times 95\% \,=\, \$456$$

It's been many years since I taught Business Math,
bit I believe I understand the terms.

$$8/10,\;4/20,\;n/30,\;\text{EOM}$$ means:
. . take an 8% discount if paid within 10 days,
. . take a 4% discount if paid within 20 days,
. . net (total amount) is due after 30 days.
The times are measured from the End Of the Month.
In this problem, EOM = November 30.

To reduce the unpaid balance to \$200,
they must pay \$256 on December 10th..

Since they are paying within 10 days,
they are entitled to an 8% discount.

So they must pay: $$\$256 \times 92\% \,=\,\$235.52$$