My question is with regards to the calculation of "Compound Interest". I have the formula below where I would get an answer to the total value of the investment over a period of "years".
- $A$ = Future value
- $P$ = Principal amount
- $R$ = Annual interest rate
- $N$ = Number of times compounded each year
- $T$ = The number of years the money is invested for
$$A = P\left(1 + \frac{R}{N} \right) ^{NT}$$
So for example if I have the following:
$P = 5,000\$$
$R = 5\%= 0.05$
$N = 12$ (Compounded monthly)
$T = 10$ years
The answer for A will be equal to $8,235.05
My question is how can I derive the equation above to account for the period of years and months? So, for example, how would I calculate $A$ if I had $T$ being equals to $T$ = $10$ years + $6$ months?
I think that the answer to the equation derivation is shown below but I'm not sure:
$$A = P\left(1 + \frac{R}{N}\right)^{N(10 + 1/2)}$$
Can anyone confirm if my calculations are correct?