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#1 2009-01-02 05:02:03
- Danbee
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- Registered: 2008-08-28
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Indeterminate forms in Calculus
A trust is established in your name which pays t+10 dollars per year for every year in perpetuity, where t is time measured in years ( here the present corresponds to time=0). Assume a constant interest rate of 4%. What is the total value, in today's dollars,of all the money that will be earned by your trust account?
Beacuse of inflation, the value of a dollar decreases as time goes on.Indeed this decrease is directly related to the continuos compounding of interest
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#2 2009-01-02 06:24:37
- mathsyperson
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- Registered: 2005-06-22
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Re: Indeterminate forms in Calculus
If you invest the money for t years, then after the end of that you'll have t(t+10) dollars.
However, because of inflation, $1 today is worth $1.04 next year, and in t years it will be worth $(1.04)^t.
To translate the t+10 dollars that you get in t years in terms of today's value, you therefore have to divide by (1.04)^t. The value is therefore given by:
I imagine this question is leading onto working out the optimum length of investment.
To do that, differentiate the above equation and find the t-value that makes dV/dt = 0.
Why did the vector cross the road?
It wanted to be normal.
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#3 2009-01-03 11:44:39
- Ms. Bitters
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- Registered: 2008-07-31
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Re: Indeterminate forms in Calculus
A trust is established in your name which pays t+10 dollars per year for every year in perpetuity, where t is time measured in years ( here the present corresponds to time=0). Assume a constant interest rate of 4%. What is the total value, in today's dollars,of all the money that will be earned by your trust account?
Beacuse of inflation, the value of a dollar decreases as time goes on.Indeed this decrease is directly related to the continuos compounding of interest
Correct me if Im wrong but would you agree that your problem is basically about determining the discounted value (or present value) of a series of payments that start at $10 at the end of Year One and then increase by $10 each year, forever; with the further stipulation that interest is i = 4%???
Last edited by Ms. Bitters (2009-01-03 12:07:09)
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