Need help solving exponential problem

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SUMMARY

The discussion centers on solving an exponential problem related to loan repayment. The specific equation presented is 3.94111..286 = (1.00178^(12 * t))/t or .286 = (e^.021341 * t)/t. Participants recommend using the Newton-Raphson method for approximating the solution, which is particularly relevant for calculating the time required to repay a loan of $10,000 at an interest rate of 2.14 percent with monthly payments of $230.

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  • Understanding of exponential equations
  • Familiarity with the Newton-Raphson method
  • Basic knowledge of loan amortization
  • Proficiency in mathematical problem-solving techniques
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  • Research the Newton-Raphson method for solving equations
  • Learn about loan amortization formulas and calculations
  • Explore numerical methods for approximating solutions to complex equations
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Mathematicians, finance professionals, students studying algebra, and anyone interested in solving exponential equations related to loan repayments.

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Hi,

I'm new to this forum so thank you in advance for any help on this problem. I would like to understand the steps needed to solve this problem. The answer is 3.94111..286 = (1.00178^(12 * t))/t or .286 = (e^.021341 * t)/t
 
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Re: need help solving exponential problem

Hi arrow, welcome to MHB!:)

In your question, I believe there's really no easy way(that I know of) to do it, but one can approximate its only solution by using the Newton-Raphson method, have you heard of this method before?
 
Re: need help solving exponential problem

Hi Anemone,

No, I'm not familiar with this method. I'll take a look. Thanks.
 
Re: need help solving exponential problem

arrow said:
Hi Anemone,

No, I'm not familiar with this method. I'll take a look. Thanks.

Oh okay...but would it be possible for you to restate the problem in its entirety here? We might be able to provide other useful advice to you if you post the full question for us first...
 
Re: need help solving exponential problem

The question was this. A person is taking out a loan of $10,000, compounded monthly, with an interest rate of 2.14 percent. She is making payments of $230 / mo. How long before the loan is repaid?
 
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