# Thread: Is This Equation Correct?

1. ## Is This Equation Correct?

Does anyone recognize this equation ...
A = P(((1 + i)n - 1)/((1-i) + (1 + i)n))

It's supposed to calculate the future value (A) of an investment (P) after n years earning an annual interest i. If this equation is not correct, what is the correct equation. How is the above equation or the correct equation derived?

In financial analysis, the Rule of 72 provides that an investment P will double (A = 2P) invested at an interest rate (i) in 72/i years (n). For example, an investment P at 9% (i) will double (A = 2P) in 8 (n) years.

Plugging .09 for i and 8 for n in the above equation does not give A = 2P.

Steve

2. ## Re: Is This Equation Correct?

link shows the formula & its derivation ...

Future Value of Annuity Formula and Calculator

3. ## Re: Is This Equation Correct?

Originally Posted by SGS
Does anyone recognize this equation ...
A = P(((1 + i)n - 1)/((1-i) + (1 + i)n))

It's supposed to calculate the future value (A) of an investment (P) after n years earning an annual interest i. If this equation is not correct, what is the correct equation. How is the above equation or the correct equation derived?

The equation that calculates future value (A)
of an invs't (P) after n years at annual rate i%
is simply: A = P(1 + i)^n

The equation you're showing deals with annuities.
(as Skeeter is telling you).

The Rule of 72 is just a guess/approximation.

4. ## Re: Is This Equation Correct?

Originally Posted by SGS
Does anyone recognize this equation ...
A = P(((1 + i)n - 1)/((1-i) + (1 + i)n))
It's supposed to calculate the future value (A) of an investment (P) after n years earning an annual interest i. If this equation is not correct, what is the correct equation. How is the above equation or the correct equation derived?
No I do not recognize that formula. The question seems to be asking for simple future value.
$\bf{A}=\bf{P}\left(1+\dfrac{\mathscr{I}}{n}\right )^{kn}$ where $\bf{P}$ is the principal invested at $\mathscr{I}$ annual % paid $\bf{n}$ times each of $\bf{k}$ years.

Example: Find the value of $\$1000$for two years at$8\%$paid quarterly? So$\bf{A}=1000\left(1+\dfrac{{0.08}}{4}\right)^{4(2) }=1171.66\$

Reading the bold above it seems that the example is just that.
If you are working a different sort of question, a present value, an annuity(a regular payment as in the link) or something other) please post an example.