Question

Find the required annual interest rate to the nearest tenth of a percent for $1200 to grow to $1800 if interest is compounded quarterly for 7 yr.

The required annual interest rate is _____ %. (Round to the nearest tenth as needed.)

Answer 1

`1200 {(1 + (r)/(4) ) }^(28) = 1800`

`{(1 + (r)/(4)) }^(28) = (3)/(2)`

`1 + (r)/(4) = \sqrt[28]{ (3)/(2) }`

`(r)/(4) = \sqrt[28]{ (3)/(2) } - 1`

`r = 4( \sqrt[28]{ (3)/(2)} - 1) = .0583`

r = 5.8%

The required interest rate is about 5.8%.