Question

3.

Your grandfather urged you to begin a habit of saving money early in your life. He

suggested that you put $5 a day into an envelope. If you follow his advice, at the end o

f

the year you will have $1,825 (365

×

$5). Your grandfather further suggested that you

take that money at the end of the year and invest it in an online brokerage mutual fund

account that has an annual expected return of

9

%.

Today you are 18 years old. If

you start following your grandfather's advice today, and

continue saving in this way the rest of your life, how much do you expect to have in the

brokerage account when you are 65 years old?

Answer 1

Formula for future value of annuity can be used to compute the future fund size as:

FV = P x [(1+r) ⁿ – 1/r]

FV = Future value of annuity

P = Periodic cash flow = $ 1,825

r = Rate per period = 9 % or 0.09 p.a.

n = Numbers of periods = 65 years – 18 years = 47 periods

FV = $ 1,825 x [(1 + 0.09) ⁴⁷ – 1/0.09]

      = $ 1,825 x [(1.09) ⁴⁷ – 1/0.09]

       = $ 1,825 x [(57.41764862 – 1/0.09]

      = $ 1,825 x (56.41764862/0.09]

      = $ 1,825 x 626.8627625

      = $ 1,144,024.54

Brokerage account will have $ 1,144,024.54 when you are 65 years old.