Question 612927

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



{{{4000=P(1+0.06/4)^(4*10)}}} Plug in {{{A=4000}}}, {{{r=0.06}}} (the decimal equivalent of 6%), {{{n=4}}} and {{{t=10}}}.



{{{4000=P(1+0.015)^(4*10)}}} Evaluate {{{0.06/4}}} to get {{{0.015}}}



{{{4000=P(1.015)^(4*10)}}} Add {{{1}}} to {{{0.015}}} to get {{{1.015}}}



{{{4000=P(1.015)^(40)}}} Multiply {{{4}}} and {{{10}}} to get {{{40}}}.



{{{4000=P(1.81401840866894)}}} Evaluate {{{(1.015)^(40)}}} to get {{{1.81401840866894}}}.



{{{4000/(1.81401840866894)=P}}} Divide both sides by {{{1.81401840866894}}} to isolate "P".



{{{P=4000/(1.81401840866894)}}} Rearrange the equation.



{{{P=2205.04928774953}}} Divide.



{{{P=2205.05}}} Round to the nearest hundredth (ie to the nearest penny).



So she should deposit <font color="red">2205.05</font> dollars into the account.