Continuously compounded interest

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In summary, the conversation revolved around finding the initial medication amount needed for continuous administration, taking into account the elimination rate of 2.5% over a period of 4 hours. The formula for continuous compounding was mentioned, but ultimately the solution was found by finding the rate and using logarithms.
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nrslmz
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Homework Statement


I must give medication to a patient continuously, but at the same time the kidneys eliminate the 2,5 per cent of the medication. I need to have 90micrograms of medication at the end of 4 hours. The initial medication amount is zero.
Normally, the limit of the compound intereset formula must be taken.


Homework Equations


The formula for continuous compounding is
Mfinal = Minitial x e^(rt)

The Attempt at a Solution


Mfinal is 90, r is -0,025, t is four and I need to find Minitial. Or is r 0,975. I try to solve the equation. I feel that I must find the rate first, like ln(Mfinal/Minitial)/t; but I can't without the initial value. Please help.
 
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  • #2
ok I sorted it out. sorry to bother.
 

Related to Continuously compounded interest

What is continuously compounded interest?

Continuously compounded interest is a method of calculating interest on a principal amount where the interest is constantly added to the principal, resulting in exponential growth.

How is continuously compounded interest different from simple interest?

Simple interest is calculated on the principal amount only, while continuously compounded interest takes into account the accumulated interest as well.

What is the formula for continuously compounded interest?

The formula for continuously compounded interest is A = Pert, where A is the final amount, P is the principal amount, e is Euler's number (approximately 2.718), r is the interest rate, and t is the time in years.

Why is continuously compounded interest used in finance and economics?

Continuously compounded interest is used because it allows for the most accurate and precise calculations of interest over time, especially when the interest rate is high or the compounding period is frequent.

What are the advantages and disadvantages of continuously compounded interest?

The advantages of continuously compounded interest include more accurate calculations, faster growth of investment, and no compounding period limitations. The disadvantages include complexity of calculations and difficulty in comparing different interest rates with different compounding periods.

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