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%.

Step-by-step explanation

We substitute the given values into the formula;


`A=P(1+(r)/(100))^t`

to obtain


`6427.35=6000(1+(r)/(100))^2`

We divide through by 6000 to obtain,


`(6427.35)/(6000)=(1+(r)/(100))^2`

This implies that,


`1.071225=(1+(r)/(100))^2`

We take the square root of both sides,


`√(1.071225)=(1+(r)/(100))`

This gives us,


`1.035=(1+(r)/(100))`

Add -1 to both sides of the equation to obtain


`0.035=(r)/(100)`

Multiply through by 100 to obtain;


`r=3.5`%


`<b>Therefore the rate is 3.5%</b>`