Lesson Problems on continuously compounded accounts

Problems on continuously compounded accounts

Problem 1

Let's calculate one year coefficients of growth: it is enough to make a selection/conclusion.


Option 1 has one year growing coefficient   =  = 1.0816.


Option 2 has one year growing coefficient  =  = 1.08058 (rounded).


Comparing, it is clear that option 1 is better (without making long calculations for 18 years).

Problem 2

Using the formula for continuously compounded account, write

    4500 = .


Divide both sides by 2000

     = .


It is the same as

    2.25 = .


Take natural logarithm of both sides

    ln(2.25) = 0.05*t,

    t =  = 16.22.


Round to one decimal place

    t = 16.2 years.    ANSWER