a. Given ????=P(1+????t),i. Solve for P.ii. Solve for ????.

Answer:i) [tex]P=\dfrac{A}{(1+r)^t}[/tex]ii) [tex]r=1-(\dfrac{A}{P})^{\frac{1}{t}}[/tex]Step-by-step explanation:Given: [tex]A=P(1+r)^t[/tex](i) solve for P for above formula. We have to isolate P from formula. [tex]A=P(1+r)^t[/tex]Divide both side by [tex](1+r)^t[/tex][tex]\dfrac{A}{(1+r)^t}=\dfrac{P(1+r)^t}{(1+r)^t}[/tex][tex]P=\dfrac{A}{(1+r)^t}[/tex](ii) solve for r. We have to isolate r from formula. Taking log both sides [tex]\log A=\log (P(1+r)^t)[/tex][tex]\log A=\log P+\log (1+r)^t[/tex]            [tex] \because \log ab = \log a+\log b[/tex][tex]\log A-\log P=t\log (1+r)[/tex]               [tex]\because \log a^m=m\log a[/tex][tex]\frac{1}{t}(\log A-\log P)=\log (1+r)[/tex][tex]\frac{1}{t}(\log (\dfrac{A}{P}))=\log (1+r)[/tex]     [tex]\because \log a-\log b=\log \frac{a}{b}[/tex][tex]\log (\dfrac{A}{P})^{\frac{1}{t}}=\log (1+r)[/tex]  [tex]1+r=(\dfrac{A}{P})^{\frac{1}{t}}[/tex][tex]r=1-(\dfrac{A}{P})^{\frac{1}{t}}[/tex]