Compound
interest formula
[tex]A=P(1+ \frac{r}{n} )^{nt} [/tex]
Where
A= Future value
P =
the Principal (the initial amount of money)
r = annual interest rate
t = time
n=
number of times compounded in one t
Remark
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r is generally a percentage like 3%, 7% etc and
are applied in the formula as 0.03, 0.07...,
the interest is compounded generally annually (n=1), quarterly (n=4),
monthly (n=12), etc...
t is in years,
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Compounding continuously means that n tends (or goes) to infinity.
As n goes to infinity, the expression [tex]P(1+ \frac{r}{n} )^{nt}[/tex] is:
[tex]\displaystyle{ \lim_{n\to\infty}P(1+ \frac{r}{n} )^{nt}=Pe^{rt}[/tex]
where e = 2.718.... (I assume this is rule 70)
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In short, when n is infinite, that is when we compound continuously, the formula is :
[tex]A=Pe^{rt}[/tex],
for P=$10,000, r=3.5/100=0.035, and t=10 years, we have:
[tex]A=Pe^{rt}=\displaystyle{ 10,000\cdot e^{0.035\cdot10}=14,190.7[/tex]
dollars.
To perform the last equation we make use of a scientific calculator.
Answer: $14,190.7
