Answer:
$2.38
Step-by-step explanation:
that's the solution I snapped for you
Time period for which person leave the money in the bank until it reaches the amount 6900 dollars is equals to 14.5 years.
"Compound interest is defined as the interest which we get on the accumulated amount of initial principal and interest which we have received for previous time duration."
Formula used
For Compound interest
[tex]A= P( 1 + \frac{r}{n}) ^{nt}[/tex]
A = final amount
P = Principal
r = rate of interest
n= number of times interest applied per period time
t=number of time period elapsed
According to the question,
Given,
Principal 'P'= 3500 dollars
Rate of interest 'r' = 4.5%
Compounded monthly 'n' = 12
Final amount 'A' = 6900 dollars
Substitute the value in the formula of compound interest to get the time,
[tex]6900 = 3500( 1+ \frac{4.5}{(12)(100))} )^{12t}[/tex]
⇒[tex]\frac{6900 }{ 3500} =( 1+ \frac{4.5}{(12)(100))} )^{12t}[/tex]
⇒[tex]\frac{69 }{ 35} =( \frac{803}{800})^{12t}[/tex]
⇒[tex]log69 -log35 = 12t( log 803-log800)[/tex]
⇒[tex]1.8388-1.5440=12t( 2.9047-2.903)[/tex]
⇒ [tex]0.2948 = 12t ( 0.0017)[/tex]
⇒[tex]t= \frac{2948}{(17)(12)}[/tex]
⇒[tex]t= 14.45[/tex]
⇒[tex]t=14.5[/tex] years
Hence, time period for which person leave the money in the bank until it reaches the amount 6900 dollars is equals to 14.5 years.
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