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Llamar borrowed $8000 at a rate of 12%, compounded semi annually. Assuming he makes no payments, how much will he go after six years? Do not round any intermediate computations, and round your answer to the nearest cent.

Respuesta :

$16097.57

Explanation:

Amount borrowed = P = $8000

rate = r = 12% = 0.12

n = number of times compounded = semi-annually

n = 2

time = t = 6 years

Let the amount he owes after 6 years = FV

Using compound interest formula:

[tex]FV\text{ = P(1 +}\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} FV\text{ = 8000(1 + }\frac{0.12}{2})^{2\times6} \\ FV\text{ = 8000(1 + }0.06)^{12} \\ FV\text{ = 8000(1}.06)^{12} \\ FV\text{ = 8000(}2.01219647184) \\ FV\text{ = }16097.5718 \end{gathered}[/tex]

To the nearest cent, the amount owed is $16097.57

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