Revision as of 01:00, 18 November 2023 by Admin (Created page with "'''Solution: D''' First, find <math>a(t)</math> <math display = "block"> a(t)=\exp \left[\int_0^t \delta_r d r\right]=\exp \left[\int_0^t \frac{r}{50} d r\right]=\exp \left[t^2 / 100\right] </math> The balance in the account at time 10 is: <math>300 a(10)+X \frac{a(10)}{a(4)}=815.48+2.31637 X</math> The total interest earned from <math>t=0</math> to <math>t=10</math> is: <math display = "block">815.48+2.31637 X-(300+X)=4 X \Rightarrow X=192.08</math>. {{soacopyright |...")
Exercise
ABy Admin
Nov 18'23
Answer
Solution: D
First, find [math]a(t)[/math]
[[math]]
a(t)=\exp \left[\int_0^t \delta_r d r\right]=\exp \left[\int_0^t \frac{r}{50} d r\right]=\exp \left[t^2 / 100\right]
[[/math]]
The balance in the account at time 10 is: [math]300 a(10)+X \frac{a(10)}{a(4)}=815.48+2.31637 X[/math] The total interest earned from [math]t=0[/math] to [math]t=10[/math] is:
[[math]]815.48+2.31637 X-(300+X)=4 X \Rightarrow X=192.08[[/math]]
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