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April 21, 2014

Homework Help: math

Posted by claudia on Wednesday, May 16, 2007 at 10:12am.

A) If the AEI increases by 3.0% a year and the RPI increases by 11.0% in the same year, then real earnings have gone down by 8%

B) A new baby's parents are given 400 to invest for the baby, to be left untouched until she is 18 years old, in an account which has a guaranteed rate of interest of at least 4.5% per annum. If no more money is put into the account, there will be at least 880 in the account at the end of a full 18 years.

C) If the CPI is 130.0 and the base year was taken as 5 years ago, then the annual rate of inflation must be 6%.

D) The cost of a stereo system is advertised with a reduction of 30%. The buyer will pay more if VAT is added on before the reduction in price, instead of VAT being added on after the reduction in price.

E) A price ratio of 1.2 corresponds to a price increase of 12%

F) An index-linked pension is worth exactly the same in real terms year after year.

Can anyone help? I think B is true and D is false??? If so what is the other true

C is false. The rate of inflation gets compounded, so the true annual rate is actually 5.38%. That is the fifth root of 1.30, minus 1.

The other statements are true, although one might make a strong case that index-linked pensions do not use a proper CPI for senior citizens. These days, the CPI tends to underestimate the true cost of living, by making lowering adjustments for improved quality of things like cars, health care and new high-tech devices. many such indexes do not properly weight fuel, food and housing costs.

thank you. I need to choose only the 2 true statements.


Two statements that are controversial or 'almost true' are A and F. C is definitely false. I am not sure how VAT taxes work, so perhaps D should be eliminated. That leaves B and E as "true".

D is tricky, it actually makes no difference.
I illustrate, suppose the stereo costs $200 and VAT is 12%

If reduction is done first
cost = 200*.7
after adding 12%, final cost = 200*.7*1.12

if reduction is done after VAT is added

cost with Vat = 200*1.12
now reduced by 30%, final cost = 200*1.12*.7

notice the calculations are the same.

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