The investment will take 7.6 years to grow to the desired amount with the preferred interest rate, compounded monthly.
Compound Interest:
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
According to the given problem,
The formula for measuring compound interest:
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex] .. (1)
Where, P = Principal
A = Amount
r = Interest rate
n = Number of times interest is compounded in one year
t = time( years )
Putting values in equation (1),
A = $1000
P = $400
r = 12%
n = 12 (compounded monthly)
⇒ [tex]1000 = 400(1+\frac{0.12}{12})^{nt}[/tex]
⇒ [tex]1000 = 400(1.01)^{12t}[/tex]
⇒ t = 7.6 years
Hence, we can conclude that the amount will take 7.6 years to grow to $1000 at 12% interest rate.
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