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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?

Dilip Sarwate
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    Yes, 10 years and 6 months is 10.5 years. – Sloan Jun 10 '15 at 17:00
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    Yes, your calculations are correct provided the exponents are as shown in the question (as edited by me). @bharb's assertions about $T$, the number of years, needing to be a multiple of $N = 12$ are based on a mis-reading of the definitions of the various symbols. – Dilip Sarwate Jun 10 '15 at 17:29
  • @DilipSarwate Yup! Too much math, too little thinking here. Comment deleted! +1 – Lonidard Jun 10 '15 at 17:31

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