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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 4℅ 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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