# Rate of appreciation: the rule?

• Nov 23rd 2006, 11:44 PM
xxpink__saltxx
Rate 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 AM
CaptainBlack
Quote:

Originally Posted by xxpink__saltxx
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

Can you be more specific

RonL
• Nov 24th 2006, 02:29 AM
xxpink__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 AM
anthmoo
Quote:

Originally Posted by xxpink__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?

Are you sure that formula is correct?
• Dec 30th 2006, 11:07 AM
topsquark
Quote:

Originally Posted by xxpink__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?

I can't get the 19.52% in either event, but is the formula:
$n^{\left ( \frac{fv}{pv} \right ) } + 1$

or

$n^{\left ( \frac{fv}{pv} + 1 \right ) }$

In any event this isn't an equation. What's this expression equal to?

-Dan
• Dec 30th 2006, 11:46 AM
earboth
Quote:

Originally Posted by xxpink__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?

Hello,

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

I understand your explanations that you want to calculate:

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

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

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

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 PM
ticbol
Quote:

Originally Posted by xxpink__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?

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
• Dec 30th 2006, 02:58 PM
topsquark
Quote:

Originally Posted by ticbol
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