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g100num [7]
3 years ago
7

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?
Mathematics
1 answer:
vlabodo [156]3 years ago
3 0
The interest rate is 3.5%.

EXPLANATION

We substitute the given values into the formula;

A=P(1+\frac{r}{100})^t

to obtain

6427.35=6000(1+\frac{r}{100})^2

We divide through by 6000 to obtain,

\frac{6427.35}{6000}=(1+\frac{r}{100})^2

This implies that,

1.071225=(1+\frac{r}{100})^2

We take the square root of both sides,

\sqrt{1.071225}=(1+\frac{r}{100})

This gives us,

1.035=(1+\frac{r}{100})

Add -1 to both sides of the equation to obtain

0.035=\frac{r}{100}

Multiply through by 100 to obtain;

r=3.5%

Therefore the rate is 3.5%
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