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The formula A equals =P left parenthesis 1 plus r right parenthesis squared (1+r)2 gives the amount A in dollars that P dollars will grow to in 2 years at interest rate r left parenthesis where (where r is given as a decimal right parenthesis comma decimal), using compound interest. What interest rate will cause $6000 to grow to $6427.35 in 2​ years?

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The interest rate is 3.5%.

EXPLANATION

We substitute the given values into the formula;

[tex]A=P(1+\frac{r}{100})^t[/tex]

to obtain

[tex]6427.35=6000(1+\frac{r}{100})^2[/tex]

We divide through by 6000 to obtain,

[tex]\frac{6427.35}{6000}=(1+\frac{r}{100})^2[/tex]

This implies that,

[tex]1.071225=(1+\frac{r}{100})^2[/tex]

We take the square root of both sides,

[tex]\sqrt{1.071225}=(1+\frac{r}{100})[/tex]

This gives us,

[tex]1.035=(1+\frac{r}{100})[/tex]

Add -1 to both sides of the equation to obtain

[tex]0.035=\frac{r}{100}[/tex]

Multiply through by 100 to obtain;

[tex]r=3.5[/tex]%

[tex]<b>Therefore the rate is 3.5%</b>[/tex]

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