Question 193100
{{{A=P(1+r/n)^(n*t)}}}  Start with the compound interest formula



{{{150000=P(1+0.055/365)^(365t)}}}  Plug in {{{A=150000}}}, {{{r=0.055}}} (this is the decimal form of 5.5% interest), and {{{n=365}}}



{{{150000=P(1+0.0001507)^(365t)}}} Divide. Note: this value is approximate. So all future calculations will be approximate.



{{{150000=P(1.0001507)^(365t)}}} Add



{{{150000/(1.0001507)^(365t)=P}}} Divide both sides by {{{(1.0001507)^(365t)}}} to isolate "P".



{{{P=150000/(1.0001507)^(365t)}}} Rearrange the equation




Now simply plug in the given values of "t" to find P:


t=1:


{{{P=150000/(1.0001507)^(365t)}}} Start with the given equation.



{{{P=150000/(1.0001507)^(365(1))}}} Plug in {{{t=1}}}



{{{P=150000/(1.0001507)^(365)}}} Multiply



{{{P=150000/(1.0565420)}}} Raise 1.0001507 to the 365th power to get 1.0565420



{{{P=141972.5860}}} Divide



So if you want to have $150,000 in the account in 1 year, you need to invest about $141,972.59 in the account.




I'll let you do the other value of t (it will follow the same procedure).