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Suppose that $2700 borrowed for two years at an interest rate of 4.5% per year, compounded continuouslyFind the amount owed, assuming no payments are made until the end. not round any intermediate computations , and round your answer to the nearest cent

Respuesta :

To find:

The amount owed.

Solution:

It is known that the amount owed when the money is compounding continuously at a rate of r per year for the time t years is given by:

[tex]A=Pe^{rt}[/tex]

Here, P = 2700, r = 0.045, t = 2, so the amount is:

[tex]\begin{gathered} A=2700e^{(0.045\times2)} \\ =2700e^{0.09} \\ =2700(1.094) \\ =2954.27 \end{gathered}[/tex]

Thus, the amount he owed after 2 years is $2954.27.

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