Use the compound interest formula a = p(1 + r) {}^t \:and the given information to solve for r. A = $2800P = $2200t = 7 r = ______% (round to the nearest hundredth)

Question

use the compound interest formula
`a = p(1 + r) {}^t \:`and the given information to solve for r. A = $2800P = $2200t = 7 r = ______% (round to the nearest hundredth)

Answer 1

The compound interest formula is

`A=P\cdot(1+r)^t`

In the exercise, we have:

A=2800

P=2200

t=7

`\begin{gathered} A=P(1+r)^t \\ 2800=2200(1+r)^7 \\ (2800)/(2200)=(1+r)^7 \\ (14)/(11)=(1+r)^7 \\ \sqrt[7]{(14)/(11)}=\sqrt[7]{(1+r)^7} \\ \sqrt[7]{(14)/(11)}=1+r \\ 1.0351=1+r \\ r=1.0351-1 \\ r=0.0351 \\ r=0.04 \end{gathered}`

Answer: 3.51%