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Trey Gorman invests $5,000 in a 1-year certificate of deposit that earns interest at an annual rate of 4% compounded monthly. The amount per $1.00 is 1.040742. How much interest will he earn at the end of one year?

Respuesta :

ClarenceV
The future value of his investment is $5,203.71. He would have earned an interest of $203.71 by the end of the year.

Answer:

The interest would be $ 203.707715

Step-by-step explanation:

Since, the amount after compounded monthly is,

[tex]A=P(1+\frac{r}{12})^{12t}[/tex]

Where, P is the principal amount,

r is the annual rate of interest,

t is time ( in years ),

Here, P = $ 5000,

r = 4 % = 0.04,

t = 1 year,

So, the amount after 1 year would be,

[tex]A=5000(1+\frac{0.04}{12})^{12\times 1}[/tex]

[tex]=5000(\frac{12+0.04}{12})^{12}[/tex]

[tex]=5000(\frac{12.04}{12})^{12}[/tex]

[tex]=5203.707715[/tex]

Hence, the interest would be,

[tex]I=A-P[/tex]

[tex]=5203.707715-5000[/tex]

[tex]=\$ 203.707715[/tex]

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