Difference

Question

A car's worth drops every year to 4/5 of the worth the year before. Today, the car's worth is 320'000 SEK.
What was the worth of the car 3 years ago?

Answer 1

Frederick:

 

Let the car be worth V,  three years ago.  In the first year, its worth is reduced to (4/5)V. In the second year it is reduced to(4/5)[(4/5)V] = (4/5)² V = (16/25)V.  In the third year it is further reduced to (4/5){(4/5)[(4/5)V]} = (4/5)³V =(64/125) V.  We are given that its worth today is 320000. (A Lamborghini?) Equate the two worths.

 

(64/125) V = 320000.

 

V = 320000 (125)/64 = 6250000 SEK

 

Dattaprabhakar (Dr. G.)

 

P.S.  After the n-th year the car's worth is (4/5)ⁿ (625000) SEK.  Got it?  (look at the words/numbers in bold, except your SEK, of course.)