Math help pleaseee
An Oil painting is worth $400 its value increases by 7% each year. What is its value in 6 years.
With the knowledge I have this would be a geometric problem and i should be doing something like
400 * 7%^6-1
7% of 400 is 28 so replace that with 28? Or maybe it's 7% on the dollar so 1.07.
Which would be...
400 * 1.07 ^6-1
But looking at the answers in the back of the book I see 600.29
I honestly think I'm missing something really obvious or something.. halp please
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September 12, 2011
11 Comments • Newest first
[quote=tiganior1]The exponent denotes the amount of terms.
Sorry, I can't help you much here, I use it more in finance than geometric mathematics.[/quote]
Ahah it's fine. Thanks for all the help.
[quote=indu95]Did you do this in Grade 11, is this similar to calculating compound interest?[/quote]
Yeaaaah, Grade 11. And it sounds exactly like compound interest. I just can't remember the formula or anything.
[quote=tiganior1]400 * (1 + 0.07)^6
(Initial value) * (1 + (Interest percentage as a decimal)^(Number of years)
Gotten off a similar formula I use for excel to calculate compound interest.[/quote]
Ahh I see, can you help me explain why I'm not doing the -1 on the term for this, for all other geometric sequences I have been required to subract 1 from the term number meaning 5.
[quote=indu95]Is there like a formula in which I could arrive there too? Because doing that way is probably not going to be accepted by my teacher[/quote]
[b]P[/b]resent [b]V[/b]alue = (Initial [b]A[/b]mount)(1+[b]R[/b]ate)^[b]T[/b]erms
PV = AR^t
600.29 = (400) (1 + 0.07)^6
*terms is equal to the number of compounding terms in a year multiplied by the number of years.
[quote=tiganior1]7% of 400 = 28
7% of 428 = 29.96
7% of 457.96 = 32.0572
7% of 490.0172 = 34.301204
7% of 524.318404 = 36.70228828
7% of 561.02069228 = 39.2714484596
7% of 600.2921407396 = 42.020449851772
$642.312590591372
~642.31
I may have added an extra iteration, depending if you count the 400 as the first year or not.[/quote]
Is there like a formula in which I could arrive there too? Because doing that way is probably not going to be accepted by my teacher
[quote=xVolcomStone]Awww, I can't remember this from last year. D:[/quote]
Did you do this in Grade 11, is this similar to calculating compound interest?
[quote=WhatssUpFool] [/quote] I see that method but there has to be a mathematical way of doing it.
Awww, I can't remember this from last year. D:
[quote=Fanaticc]you didnt consider the fact that u have to consider 7% of every increased number/year. When it goes up 7% to 428, you didnt consider 7% of 428, but rather 400. and so on. Because 7% of 428,456,etcetc isnt 28.[/quote]
So how do I do this problem then o-o
P=ert right? Lol I totally forgot.
It's original cost(1+percent change)^time rate thing.
The percent change can be minus if it decreases in value.
The time change is like if it increases seven times a year and we wait two years then the exponent would be 14.
[quote=OscarTheOrca]568. 7% of 400 is 28.
28 X 6 = 168.
168 + 400 = 568.
I'm pretty darn sure it's $568.00.. But your book says $600.29? Maybe you're looking at the wrong section of the answers.. Or your question isn't an odd number.[/quote]
Yeah, I like checked if I was looking in the wrong section for like the past hour, I don't get where I went wrong I'm getting 568 aswell.. Ahh!
Your process is right, but don't subtract 1 term. It's 6 years, so 6 terms are needed.
(400)(1.07^6)
EDIT: Never mind, what you're doing is wrong. Keep in mind that each year, its value increases by 7% of its CURRENT value.
Meaning you need to use exponents to represent this gradual increase. 7% of 400 is indeed 28...
But you have to repeat this process for 6 years. In other words, 400 x 107%, then 428 x 107%, etc.