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,
In our problem:
A= 30 000
P =20 000
r = 15%=0.15
time = t = ?
n= 4
applying the formula:
[tex]A=P(1+ \frac{r}{n} )^{nt}\\\\30,000=20,000(1+ \frac{0.15}{4} )^{4t}\\\\ \displaystyle{\frac{30,000}{20,000} =(1.0375)^{4t}[/tex]
[tex] \displaystyle{ 1.5={(1.0375^4)}^t\\\\[/tex]
[tex] 1.5=1.159^t\\\\ \displaystyle { t=log_{1.159}1.5=2.75[/tex]
75% of 12 months is 3/4 of 12 months, which is 9 months
Answer: 2 years, 9 months
