How do I calculate the interest rate I have earned

R

Redshoes

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I bought shares in Vanguard Index in June 2006 for $3000. Those shares are now worth $5000. Does anybody know a formula that I can use to calculate:
1. Total interest accumulated over the total period
2. Interest accumulated per year (per year over a period of 8 years)
Thanks.
 
Can you elaborate on what you mean? Shares don't accrue interest. Are you looking to compare your capital gain on the shares with some sort of equivalent interest rate?
 
Deep breath....
R=((FV/IV)^(1/y)-1)*100
Where R is annual % rate of return
FV final value
IV initial value
y number of years(can be a fraction of a year)

So,
R=((5000/3000)^(1/7.83)-1)*100
 
Vandriver thanks for your reply and formula. I just need a little help deciphering the abbreviations:
Annual rate of return = Final Value/Initial value
then what does the sign ^mean?
the I understand (1/y)-1
the what does * mean?
Appreciate you taking the time to help me!
 
correcting typos in my reply

Vandriver thanks for your reply and formula. I just need a little help deciphering the abbreviations:
Annual rate of return = Final Value/Initial value
then what does the sign ^mean?
then I understand (1/y)-1
then what does * mean?
Appreciate you taking the time to help me!
 
Pipped to the post, but anyway:

The ^ is exponentiation or "raised to the power of". The * is multiplication. Here it is long hand:

gif.latex


If you were to put it in a cell in Microsoft Excel or Google Spreadsheet it would look like this:

=(POWER(5000/3000,1/7.83)-1)*100

to see a spreadsheet you can edit with your own figures.


The OP also asked how to calculate the return for a given year. This is given by:

gif.latex


The spreadsheet formula can also be seen in the link above. Assuming a fixed annual percentage rate of return, the return in the first eight years are:
€202.24, €215.88, €230.43, €245.97, €262.55, €280.25, €299.14, €319.31
 
Dub nerd

That is very handy. I have not been able to figure out how to do that, and always worked it out roughly.

Brendan
 
:eek: I more or less understand the concept of compound interest but I look at this thread and it becomes more clear to me why I didn't ever really "get" investing. :confused: Maybe I shouldn't have given up honours maths when I got to 5th year after all!

Anyway, I can kind of follow the above but why the minus 1 in the equation? Sorry to be asking what might be obvious to the less mathematically challenged.
 
I just use a compound interest calculator, haven't verified if it is correct but it seems about right
http://www.moneychimp.com/calculator/compound_interest_calculator.htm

Usually I'd use this to calculate the future value.

But in the case of the query in first post in this thread we know the "future" value and can work backwards
Current principal is 3000
Annual addition is 0
Years to grow is 7.83 (June 2006 to April 2014)

You can then play around with the interest rate until it gives a future value of 5000. Based in this the interest is somewhere between 6.74 and 6.75%
 
Janet said:
:eek: I more or less understand the concept of compound interest but I look at this thread and it becomes more clear to me why I didn't ever really "get" investing. :confused: Maybe I shouldn't have given up honours maths when I got to 5th year after all!

Anyway, I can kind of follow the above but why the minus 1 in the equation? Sorry to be asking what might be obvious to the less mathematically challenged.
Click to expand...
The first part of the sum gives a result of 1.067.. To convert this to a %age increase,minus 1 to get .067 then multiply by 100 to get 6.7%
The 1.067 would be the annual multiplication factor.
 
+1. It's much easier to work with a multiplication factor R. The relationship between R and what we normally think of as a percentage rate is Rate = (R - 1) x 100. If P is the initial principal value, and n the number of years, the two equations from earlier get much simpler:

gif.latex



You can see that both are straightforwardly related to the familiar compound interest formula:
gif.latex
 
Redshoes said:
I bought shares in Vanguard Index in June 2006 for $3000. Those shares are now worth $5000. Does anybody know a formula that I can use to calculate:
1. Total interest accumulated over the total period
2. Interest accumulated per year (per year over a period of 8 years)
Thanks.
Click to expand...

How to do it on excel:

Type into cells:
Number of periods: 8
Payment per period: 0
Present Value: 3000
Future period: 5000
End or Beginning: 0

In a new cell, type =rate( Excel will then tell you the order it wants to you fill in the details.

=rate(number of periods, PV, FV, End) = 6.59%

You can do the same for calculating future value, discounting back etc. Excel will always tell you what order to put the information into the formula for you.

Steven
www.bluewaterfp.ie
 
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