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Allisa [31]
3 years ago
10

you invest $1300 in an account at interest rate r, compounded continuously. Find the time required for the amount to double and

triple. (Round your answers to two decimal places.) r = 0.074
Business
1 answer:
miskamm [114]3 years ago
4 0

Answer:

  • 1. <em>For the amount to double</em>: <u>9.37 years</u>
  • 2. <em>For the amount to triple</em>: <u>14.85 years</u>

Explanation:

The equation for continuosly compounded interest is:

  • F=P\times e^{rt}

Where:

  • P is the amount that you invest today: $1,300
  • F is the value after t years: the double or triple of $1,300
  • r is the annual interest rate: 0.074

<u>1. For the amount to double:</u>

Substitute the values and solve for t:

             2\times \$1,300=\$1,300\times e^{0.074t}\\ \\ 0.074t=\ln 2\\ \\ t=\ln 2/0.074=9.37years

<u>2. For the amount to triple:</u>

<u />

            3\times \$1,300=\$1,300\times e^{0.074t}\\ \\ 0.074t=\ln 3\\ \\ t=\ln 3/0.074=14.85years

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Answer:

Jones is liable to pay.

He is liable to pay to the tune of $1000. This may be negotiated however if it is not fair.

Explanation:

See the following points

  • The question above is an example of Implied At-law contracts. (We will get to the definition of this in a bit).
  • A contract is a legally binding agreement that recognises and governs the rights and duties of the parties to the agreement. A contract is legally enforceable because it meets the requirements and approval of<u> the Law</u>. From the above definition it is clear that two people may actually be engaging  in a contract without knowing it.
  • The law defines that a contract is.
  • Contracts may be Express or Implied.
  • Express contracts are simply contracts that are stated expressly, or openly, in either writing or orally, at the time of contract formation.
  • Implied contracts are created when two or more parties have no written contract.
  • There are two types of implied contracts:

  1. Implied In-Fact Contracts: these are contracts which create an obligation between the parties based on the facts of the situation. For example, assume your neighbor hires you to wash his car every Friday for the entire holidays. You wash your neighbor’s car for the first four weekends of the holidays and get paid on Friday morning each time. The fifth Friday you wash the car and when you arrive at your neighbor’s house for your pay, your neighbor refuses to pay you.                                           The law will infer that there is a contract between you and your neighbor, even though you never put anything in writing. This is an implied in-fact contract.

       2. The other type of Implied contract is that which is Implied At-Law

In the case between Jones and Smith, the law imposes a duty to perform a contract, and will enforce such a contract even against a person’s will, where the situation is such that without this legal intervention, one party would be <u>unfairly enriched</u> or advantaged by another party’s action.

  • In the question above, Smith is a CPA. He is qualified in every respect to carry out Professional Tax services. His services may be relied upon with a great degree of confidence.
  • If Jones had not filed those tax returns, he probably would have lost monies that should have accrued to him from the government.

This type of agreement is also considered a quasi-contract. A quasi-contract occurs where the law imposes an obligation upon the parties where in fact the parties did not intend to enter into a contract and made no promise to perform.

However, because one party would be unjustly enriched by another party’s action, the beneficiary of those actions must make restitution or pay fair value for the services provided, even though there was never any intention to enter into an agreement.

Cheers!

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