SOLUTION: I need help trying to solve this problem, Thanks Problem : What is the amount P that must be invested at interest rate 5.5% compounded daily to obtain the balance of A =$15

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Question 193100: I need help trying to solve this problem, Thanks
Problem :
What is the amount P that must be invested at interest rate 5.5% compounded daily to obtain the balance of A =$150000 in t years.
t = 1 P=?
t= 10 P=?
Given is the interest rate formula A=P(1+(r/n))^nt
Any help with this question will be greatly appreciated, thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A=P%281%2Br%2Fn%29%5E%28n%2At%29 Start with the compound interest formula


150000=P%281%2B0.055%2F365%29%5E%28365t%29 Plug in A=150000, r=0.055 (this is the decimal form of 5.5% interest), and n=365


150000=P%281%2B0.0001507%29%5E%28365t%29 Divide. Note: this value is approximate. So all future calculations will be approximate.


150000=P%281.0001507%29%5E%28365t%29 Add


150000%2F%281.0001507%29%5E%28365t%29=P Divide both sides by %281.0001507%29%5E%28365t%29 to isolate "P".


P=150000%2F%281.0001507%29%5E%28365t%29 Rearrange the equation



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

t=1:

P=150000%2F%281.0001507%29%5E%28365t%29 Start with the given equation.


P=150000%2F%281.0001507%29%5E%28365%281%29%29 Plug in t=1


P=150000%2F%281.0001507%29%5E%28365%29 Multiply


P=150000%2F%281.0565420%29 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).