It will take 7 years for the account balance to reach $11,688.69.
To find how long will it take for the account balance to reach $11,688.69
we will use the compound interest formula that is
[tex]$ \text A = \text P(1 + \frac{\text r}{\text n})^{\text {nt}}[/tex]
where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Given that, P = $7,171
A = $11,688.69
r = 7%
n = 12
t = to find
Substitute the details in the formula and we get
[tex]$11688.69 = 7171(1 + \frac{0.07}{12})^{12t}[/tex]
[tex]$ \text t=\frac{\log _{\frac{1207}{1200}}\left(\frac{1168869}{717100}\right)}{12}[/tex]
t = 7.000003 = 7 years
Thus, It will take 7 years for the account balance to reach $11,688.69.
Learn more about compound interest
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