Question

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?

Answer 1

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;

$r=3.5$%

$Therefore the rate is 3.5%$