continuous compound problem

Question

How much would a person have to invest at 4.5% compounded continuously to have $10,000 five years from today?

Answer 1

Not sure why the 2 down votes(?)

 

The continuously compounding formula is derived from F=P(1+r/n)^nt  where n is the number of compounding periods per year, as you let n->∞:

 

  F = Pe^rt

 

  F = future value of investment

  P = present value of investment

  r = interest rate (annual rate) as a decimal

  t = number of years

 

 F = 10000 = Pe^(0.045)(5)

        

       ln(10000) = ln(P) + (0.045)(5)

       9.2103404-0.225 = ln(P)

       8.9853404 = ln(P)

       P = e^8.9853404

       P = 7985.16

 

 

Check:

      7985.16*e^0.045*5 = 9999.997