can anyone help me with a rule for rate of appreciation? I have a rule except i dont think im putting it into my calculator right i keep getting overally large numbers.

Thanks

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- Nov 23rd 2006, 11:44 PMxxpink__saltxxRate of appreciation: the rule?
can anyone help me with a rule for rate of appreciation? I have a rule except i dont think im putting it into my calculator right i keep getting overally large numbers.

Thanks - Nov 24th 2006, 12:37 AMCaptainBlack
- Nov 24th 2006, 02:29 AMxxpink__saltxx
well my question is: the value of a stamp increases from $700 to $1000 in 2 years. What is the rate of appreciation?

Sorry i was a little late replying

my formula is: n ^(fv/pv)+1

n=time

^ = square root sign (cant find one on the keyboard)

fv= future value

pv=present value

When i put my above values in i get this: 2^(1000/700)+1 = 3.39

The answer on my sheet is actually 19.52% p.a.

How do i get that? - Dec 30th 2006, 10:15 AManthmoo
- Dec 30th 2006, 11:07 AMtopsquark
- Dec 30th 2006, 11:46 AMearboth
Hello,

you wrote: "...my formula is: n ^(fv/pv)+1"

I understand your explanations that you want to calculate:

$\displaystyle \sqrt [n]{\frac{fv}{pv}}+1$

The 2nd root is the same as the good ol' square-root.

$\displaystyle \sqrt[2]{\frac{1000}{700}}+1 \approx 2.1952286 $

Look at the increase: You find 0.1952286 and that's the same as 19.52%.

By the way: I don't understand**what**you want to calculate, I can only show you**how**to get the result.

EB - Dec 30th 2006, 01:27 PMticbol
Here is one way.

I don't know your formula but a few play showed it came from the simple formula

A = P[(1+r)^n]

where

A = total amount in n years-----------------your Fv

P = initial amount, or amount in zero year----your Pv

r = rate of interest per year------------------your rate of appreciation

n = number of years

------------

Since it is vacation time, lots of sparetime, let us review how that simple formula was derived.

0 year:

Ao = P

After 1 year:

A1 = P +P*r = P(1+r)

After 2 years:

A2 = P(1+r) + [P(1+r)]*r = [P(1+r)](1+r) = P[(1+r)^2]

....After n years:

An = P[(1+r)^n]

----->>> "Ao, A1, A2....An" are read "A sub 0", "A sub 1", "A sub 2"...."A sub n"

----------------------------

So you have

Fv = (Pv)[(1+r)^n]

Divide both sides by Pv,

(Fv)/(Pv) = (1+r)^n

To isolate r, get the nth roots of both sides,

[(Fv)/(Pv)]^(1/n) = 1+r

Hence,

r = [(Fv)/(Pv)]^(1/n) -1 ---------------(i), it is minus 1.

Yours is +1, that's why you're getting wrong answers from your calculator.

So, with n=2,

r = [1000/700]^(1/2) -1

r = 1.1952 -1

r = 0.1952

r = 19.52 percent ---------------answer. - Dec 30th 2006, 02:58 PMtopsquark