Calcululus/financial maths

[Karabo]

The rate of change of the value of an investment, S, with respect to time, t ≥ 0, is given by dS dt =1000r 10ert/100, where r is the annual interest rate (assumed constant) and the principal of the investment is S(0) = 10 000.

(a) Find an expression for S(t), that is, the value of the investment at time t.

(b) Verify that your expression for S(t) is correct by computing S(t).

(c) Explain why S(t) is continuous for t ≥ 0.

(d) Determine, by computing lim t→∞S(t), what would happen to the value of the investment if t were to grow without bound. Interpret the result.
(e) How long would it take for the value of the investment to be exactly 15 000?

 

[Deleted member 4993]

The rate of change of the value of an investment, S, with respect to time, t ≥ 0, is given by dS dt =1000r 10ert/100, where r is the annual interest rate (assumed constant) and the principal of the investment is S(0) = 10 000.

(a) Find an expression for S(t), that is, the value of the investment at time t.

(b) Verify that your expression for S(t) is correct by computing S(t).

(c) Explain why S(t) is continuous for t ≥ 0.

(d) Determine, by computing lim t→∞S(t), what would happen to the value of the investment if t were to grow without bound. Interpret the result.
(e) How long would it take for the value of the investment to be exactly 15 000?

Please check your equation for correctness. As displayed in the post - it does not make sense. May be you could post a picture of your assignment for better clarity.

In addition, please show us what you have tried and exactly where you are stuck.

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https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[Karabo]

This is the picture if the assignment i am still working on my answers then i will post my progress here because i am not really sure how to tackle the question

 

[Deleted member 4993]

This is the picture if the assignment i am still working on my answers then i will post my progress here because i am not really sure how to tackle the question

Tackle the questions as those are given to you. For 1(a), you need to integrate \(\displaystyle \frac{dS}{dt}\) to calculate expression for S.



continue.....

 

[Karabo]

This is what i have done first