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Nicole opens a savings account with an initial deposit of $5,000. since then, she has never made any other deposits or withdrawals. her savings account earns 4â„… intrest compounded monthly. which equation gives the approximate amount, A(x), she has in her savings account as a function of x, the number of years since her initial deposit?

1. A(x)= 5,000^(0.96x)

2. A(x)= 5,000(0.959)^x

3. A(x)= 5,000 + 0.04x

4. A(x)= 5,000^(1.04x)

5. A(x)= 5,000(1.041)^x​

Respuesta :

calculista

Answer:

Option 5.  [tex]A(x)=\$5,000(1.041)^{x}[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=x\ years\\ P=\$5,000\\ r=0.04\\n=12[/tex]  

substitute in the formula above  

[tex]A=\$5,000(1+\frac{0.04}{12})^{12x}[/tex]  

[tex]A=\$5,000(1.041)^{x}[/tex]  

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