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Sagot :
The formula for compound interest would be:
[tex]A=P(1+r)^t[/tex]Where
A is the amount accumulated after a time
P is the principal amount deposited
r is the rate of interest (in decimal)
t is the time in years
Given,
P = 4500
r = 2.5%/100 = 0.025
A = 22,960.83
Now, we substitute and solve for t using natural logs. Shown below:
[tex]\begin{gathered} A=P(1+r)^t \\ 22,960.83=4500(1+0.025)^t \\ 22,960.83=4500(1.025)^t \\ 5.1024=1.025^t \end{gathered}[/tex]Now, we take natural log (Ln) of both sides and solve for t :
[tex]\begin{gathered} \ln (5.1024)=\ln (1.025^t) \\ \ln (5.1024)=t\ln (1.025) \\ t=\frac{\ln (5.1024)}{\ln (1.025)} \\ t=65.99 \end{gathered}[/tex]So, the money was approximately 66 years old.
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