what amount must you invest today at 5% compounded annually for it to grow to $2000 in 3 years?

Question

please show me step by step on how to solve it

Answer 1

Start with the formula for compound interest:

 

A = P*(1 + r/n)^nt

 

Where

• A = the final amount of money = $2000
• P = the principle, or initial amount of money invested = unknown
• r = the interest rate expressed as a decimal = 5% = 0.05
• n = the number of compounding per year = annual = 1
• t = years = 3

Now plug in the numbers and solve for P:

 

      A = P*(1 + r/n)^nt

      $2000 = P*(1 + 0.05/1)^1*3

      $2000 = P*(1.05)³

      $2000 = P*(1.157625)

      $2000/(1.157625) = P

 

      $1727.68 = P