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Sagot :
Given that Dani has 2000 in a investment account that earns 3% per year compound monthly.
Part A).
The compound interest formula:
Compound interest can be calculated using the formula
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]where,
A(t) is the account value,
t is measured in years,
P is the starting amount of the account, often called the principal, or more generally present value,
r is the annual percentage rate (APR) expressed as a decimal, and
n is the number of compounding periods in one year.
Now, Part B).
initial amount = 2000
annual percentage rate = 3%
Compounding period = 12
So,
[tex]A(t)=(1+\frac{r}{n})^{nt}[/tex]Further,
[tex]\begin{gathered} 3500=2000(1+\frac{0.03}{12})^{12t} \\ \frac{3500}{2000}=(1+\frac{0.03}{12})^{12t} \\ \ln 1.75=12t\ln 1.0025 \\ t=\frac{1}{12}\frac{\ln 1.75}{\ln 1.0025} \\ t=18.67 \end{gathered}[/tex]Hence, t = 18.67 is the answer for part B.
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