The value of the account to reach $13,140 will take 14 years assuming no deposits or withdrawals are made .
What is compound interest?
Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.
Formula of compound interest :
[tex]A = P (1+ \frac{r}{100} )^{n}[/tex]
Where,
A = final Amount
P = initial principal
r = rate per annum
n = time in years
According to the question
Camden invested (P) = $7,200
Interest rate per month (r) = 4.4%
Amount to reach = $13,140
now , using Formula of compound interest
[tex]A = P (1+ \frac{r}{100} )^{n}[/tex] ere , n = n/12 (as concluding monthly wise )
Substituting the values
[tex]13140 = 7200 (1+ \frac{4.4}{100} )^{\frac{n}{12} }[/tex]
1.825 = [tex](1+ \frac{4.4}{100} )^{\frac{n}{12} }[/tex]
1.825 = [tex](1..044 )^{\frac{n}{12} }[/tex]
n ≈ 168 months (approx.)
n = 14 years (nearest year)
Hence, the value of the account to reach $13,140 will take 14 years assuming no deposits or withdrawals are made .
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