Answer:
She deposit $2300 (approx.)
Step-by-step explanation:
Given: Rate, R = 3.1 % compounded monthly.
Time, T = 5 year
Amount, A = $ 2685.08
To find: Deposit amount i.e., Principal value ( P )
We use Compound interest Formula,
[tex]A=P\times(1+\frac{R}{100})^n[/tex]
where n = no of times interest is calculated during time period.
Here, n = 12 × 5 = 60 and R= [tex]\frac{3.1}{12}[/tex]
Let P be the Principal value or deposit amount.
Substituting given value of A, R and n. we get,
[tex]2685.08=P\times(1+\frac{\frac{3.1}{12}}{100})^{60}[/tex]
[tex]2685.08=P\times(1+\frac{3.1}{12\times100})^{60}[/tex]
[tex]2685.08=P\times(1+\frac{3.1}1200})^{60}[/tex]
[tex]2685.08=P\times(\frac{1200+3.1}{1200})^{60}[/tex]
[tex]2685.08=P\times(\frac{1203.1}{1200})^{60}[/tex]
[tex]2685.08=P\times(1.0025833)^{60}[/tex]
[tex]2685.08=P\times(1.16748438)[/tex]
[tex]P=\frac{2685.08}{1.16742438}[/tex]
[tex]P=2300.00336[/tex]
P = $ 2300 (approx.)
Therefore, She deposit $2300 (approx.)
