Question 177262
{{{A=P(1+r/n)^(nt)}}} Start with the compound interest formula where A is the return, P is the principal (the amount invested), r is the interest rate, n is the compound frequency, and t is the time (in years)



{{{350=200(1+r/1)^(1*5)}}} Plug in {{{A=350}}}, {{{p=200}}}, {{{n=1}}}, and {{{t=5}}}



{{{350=200(1+r/1)^5}}} Multiply



{{{350=200(1+r)^5}}} Reduce



{{{350/200=(1+r)^5}}} Divide both sides by 200.



{{{1.75=(1+r)^5}}} Divide.



{{{root(5,1.75)=1+r}}} Take the 5th root of both sides.



{{{1.1184=1+r}}} Take the 5th root of 1.75 to get 1.118 (this is approximate)



{{{1.1184-1=r}}} Subtract 1 from both sides.



{{{0.1184=r}}} Combine like terms.



So the answer is {{{r=0.1184}}} which is roughly 11.84%



So the interest rate needed is about 11.84%