Continuous compound interest

The interest earned is continuously added to the principle and hence both the original principal and the interest earned earn interest at the same rate.

Formula

F = P e^rt (future value)
P = F e^-rt (present value)

where

P = principal
F = future value OR accumulated amount
r = annual interest rate (a.p.r.)
t = time in years

Example: Suppose $1,000 is deposited in an account earning continous compound
interest at an annual rate of 8%. Compute the amount of money accumulated
in 10 years.

F = Pe^rt = $1,000 e^0.08(10) = $2,225.54

Example: Suppose some money is deposited in an account earning continuous
compound interest at an annual rate of 8% compounded quarterly. How
much money must be invested now in order to accumulate $1,000
in 10 years ?

F = Pe^rt = $1,000 e^-0.08(10) = $449.32

Exercises


(1) Find the amount of money accumulated if $10,000 is deposited 
    in an account paying an annual interest rate of 6% compounded
    continuously for 10 years.
     $16,000.00
     $17,908.48
     $18,140.18
     $18,221.19 


(2) Find the present value of $10,000 due in 10 years invested
    at an annual interest rate of 6% compounded continuously. 
     $5,488.12 
     $5,512.62
     $5,583.95
     $6,250.00

Calculator

Amount
Annual interest rate as a decimal
Length of the investment in years

Future value
Present value