assume that the 10% per annum is compounded monthly.

Question

Using the formulae for geometric sequences and series, show that an initial investment of $1000 plus $200 invested at the end of each month would grow to approximately $160000 (to the nearest $5000)over 20 years.

Answer 1

P(1 + r)Y + c[ ((1 + r)Y + 1 - (1 + r)) / r ]

 

P = 1000, r = 10%/12 = 0.1/12 = 1/120 = 0.08333333....

 

Y = 240 = 12 x 20 months

 

c = 200

 

 

 

Note that (1 + r) = 1 + 1/120 = 121/120

   (1+r)^y = (121/120)^240 = 7.328074