Question

Math of Finance

You decided to quit smoking today.

*basic information* Now that you are going to save 200 €/month, you decided to save those 200€ per month in a bank account that offers a 3% interest rate compounded monthly, till the day you retire (that is to say, in 20 years)

If you decide to do your deposits at the end of every month (your first deposit will be in one month from today) in a bank account that offers a 3% interest rate compounded monthly, and the deposits will increase in a 0.1% month after month, and you keep on doing so for the next 20 years:

a) Draw the timeline (at least the first five periods) with its corresponding numeration of periods and cashflows in their corresponding points

b) How much money will you have at the end? Show the workout

c) What would happen if the growth rate and the interest rate is the same?

Answer 1

This is an example of a growing annuity. And we are required to find the future value of the following growing annuity.

a) Timeline (at least the first five periods) with its corresponding numeration of periods and cashflows in their corresponding points

b) Future value of Growing Annuity =  

FVGA = C1* [((1+r)^n - (1+g)^n) / (r-g)]

C1 = 200
r (3%) = 0.0025 (3/12)
g = 0.001
n = 240 (12*20)
Therefore, FVGA will be :
200 * [((1+0.0025)^240 - (1 + 0.001)^240) / (0.0025 - 0.001)] = 73287.77

c) If the growth rate and interest rate are equal then the equation won't work as both the rates would offset each other in the timeline and cashflow would be undefined.