Question 676947


{{{A=P(1+r/n)^(n*t)}}} Start with the compound interest formula



{{{25000=10000(1+r/2)^(2*20)}}} Plug in {{{A=25000}}}, {{{P=10000}}}, {{{n=2}}} and {{{t=20}}}.



{{{25000=10000(1+r/2)^(40)}}} Multiply {{{2}}} and {{{20}}} to get {{{40}}}.



{{{25000/10000=(1+r/2)^(40)}}} Divide both sides by {{{10000}}}.



{{{2.5=(1+r/2)^(40)}}} Evaluate {{{25000/10000}}} to get {{{2.5}}}.



{{{root(40,2.5)=1+r/2}}} Take the 40th root of both sides.



{{{1.02317165469772=1+r/2}}} Take the 40th root of {{{2.5}}} to get {{{1.02317165469772}}}.



{{{1.02317165469772-1=r/2}}} Subtract 1 from both sides.



{{{0.0231716546977176=r/2}}} Combine like terms.



{{{2*0.0231716546977176=r}}} Multiply boths sides by {{{2}}} to isolate "r".



{{{0.0463433093954353=r}}} Multiply {{{2}}} and {{{0.0231716546977176}}} to get {{{0.0463433093954353}}}.



{{{r=0.0463433093954353}}} Rearrange the equation.



{{{r=0.0463}}} Round to the nearest ten-thousandth.



So the interest rate is 4.63% (multiply by 100 to convert to a percentage)