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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Thus, in our problem, P=$200, r=22%=0.22, n=4,
t=3
Applying the formula we have:
[tex]A=P(1+ \frac{r}{n} )^{nt} [/tex]
[tex]A=200(1+ \frac{0.22}{4} )^{4\cdot3}=200(1+0.055)^{12}=200(1.055)^{12}=200\cdot 1.9[/tex]
=380 ($)
Answer: 380$
