Thursday, January 9, 2014

9 Jan Thursday Lesson Summary

Points to remember from previous lessons:

- Don't state the obvious
     ~> eg. 5 years = 60 months X

- Rate and Duration MUST be in the same time frame.
     ~> keep them exact

- Foreign exchanges are Ratios :D
  eg. 1 euro = S$1.7306
        US$ 1 = S$1.3021
* to compare ratios, there must be a same BASE. *
therefore, 
        S$ 1 = US$ (1/1.3021)
        1 euro = US$ (1.7306 x 1/1.3021)
        1 euro = US$ (1.7306/1.3021)
So, we get: US$ 1 = (1.3021/1.7036) euro
                              = 0.7524 euros (to 4dp)

For interests, always write the formula first! (presentation is important~)

Simple Interest = (principal x rate x duration) / 100

Compound interest = Principal (1 + r/100)^duration

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Tax: GST

A restaurant bill came to $300. Find the total bill if there is a 10% service charge and a 7% GST added to the bill.

Bill = $(300x1.1x1.07)
       = $353.10

What if there is a 5% discount given on the bill. What is the amount payable then?

Bill = $(300x1.1x1.07x0.95)
       = $335.45
# discount doesn't make a difference no matter when it is added since it is multiplied.
   -> although the order can determine which party benefits from it.

Income tax~
Tax salary = balanced leftover pay per annum after deduction of tax relief.
Eg. Tax salary = $34 750
       Tax bill = $200 + ($4750 + 3.5/100)
(Tax bill = payment for 1st $30 000 + payment for next $10 000)


Question to think about:

When two variables, A and B, increase or decrease at the same time, it is directly proportional (y=kx) but when one increases and one decreases, it is supposedly indirectly proportional (y=k/x). But is there a way to make it directly proportional when one variable increases and the other decreases?

Discussion's on the next lesson :)


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