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I am having trouble understanding where the numbers are coming from in this question. John and Melissa wonder about the potential increase in the value of their house. Assuming a 6% appreciation per year, the formula for the value of the house after years is math formula , where starts from 0.

  1. Where did the 53 over 50 come from?
  2. Why couldn't I just calculate 6% of 219,000 for 13,140$ a year and multiply by 3 and add that to the original value?
  3. 53\50 is in parenthesis so I should divide that first? then apply the power of 3?
EvilTwinkie
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  • $\frac {53} {50} = 1.06$, that's the same as saying an increase of $6%$ – Alan Jan 11 '15 at 02:07
  • but isn't .06 6%? or for example .10 = 10% – EvilTwinkie Jan 11 '15 at 02:09
  • Which country are you from . In the first place, I do not know why would represent 1.06 as $\frac{53}{50}$. and asking for meaning of 53 and 50?. Quite strange! – Satish Ramanathan Jan 11 '15 at 02:09
  • I'm not asking the meaning of 53 over 50 I just don't understand where they got those numbers from for the formula in relation to the word problem. Also from USA – EvilTwinkie Jan 11 '15 at 02:11
  • 53/50=1.06=106% of the value or 6% INCREASE from that value – Teoc Jan 11 '15 at 02:12
  • Usually in these problems $1.06$ is left as a decimal. It's strange that your book converted it to a fraction. – GFauxPas Jan 11 '15 at 02:23
  • @GFauxPas - Maybe because it's better mathematical practice to use fractions than decimals, and it's consistent with the conventions used by the book the OP is reading? It may be uncommon, and possibly even unnecessary in this specific example, but it's more pure :-) Plus the conversion is always fraction -> decimal, decimal is the fallen, bastard child of a fraction ;-) – Benjamin R Jan 11 '15 at 02:35
  • Writing $\frac{53}{50}$ instead of $1.06$ is purely silly. A decimal is a fraction, indeed the full name is "decimal fraction." – André Nicolas Jan 11 '15 at 03:28

1 Answers1

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1) $$\dfrac{53}{50}=1.06=\text{6% increase or 106% of the corrent value}$$ 2) It is because for example, at $n=2$, the function calculates $6$% OF THE CURRENT VALUE, not the first value, $219000$. Eg at $n=2,$ it would increase by $6$%, to $\$232776$, then increase $6$% FROM $\$232776$ to $232776\times 1.06$

3) It does not matter,$$ \left( \frac{53^n}{50^n}\right)=(1.06)^n$$

Teoc
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  • That makes so much more sense now thank you. So its 106% because it is 100% of the value plus 6% more? it seems a little confusing but makes sense I suppose. – EvilTwinkie Jan 11 '15 at 02:15
  • @EvilTwinkie yep! If you want to try to apply the same logic try to find the equation for a 6% decrease :) – Teoc Jan 11 '15 at 02:16
  • You should get $219000(0.94)^n$ – Teoc Jan 11 '15 at 02:23