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A person invests 7500 dollars in a bank. The bank pays 6% interest compounded semi-annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 16200 dollars?

Respuesta :

calculista

Answer:

[tex]13.0\ years[/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=?\ years\\ P=\$7,500\\ r=0.06\\n=2\\ A=\$16,200[/tex]  

substitute in the formula above  

[tex]16,200=7,500(1+\frac{0.06}{2})^{2t}[/tex]  

[tex](2.16)=(1.03)^{2t}[/tex]  

Apply log both sides

[tex]log(2.16)=(2t)log(1.03)[/tex]  

[tex]t=log(2.16)/[(2)log(1.03)][/tex]  

[tex]t=13.0\ years[/tex]  

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