Answer: $ 1909.822 ( approx )
Step-by-step explanation:
Here, Principal amount = $ 200,
The rate per period (week) = 5 %
Let us take the years after first year,
Thus, time = 0 to 7 years ( We estimate the time after first year )
Hence, the total sum of the amount from first year to eighth year,
[tex]S = \sum_{t=0}^{t=7} 200(1+\frac{5}{100})^t[/tex]
[tex]= \sum_{t=0}^{t=7} 200(1+0.05)^t[/tex]
[tex]= \sum_{t=0}^{t=7} 200(1.05)^t[/tex]
[tex]=200(1.05)^0+200(1.05)^1+200(1.05)^2+200(1.05)^3+200(1.05)^4+200(1.05)^5+200(1.05)^6+200(1.05)^7[/tex]
[tex]=200+210+220.5+231.525+243.10125+255.2563125+268.019128125+281.420084531[/tex]
[tex]=1909.82177516\approx 1909.822[/tex]
Therefore, she has approximately 1909.822 dollars after 8 weeks.
