Question

I am 28 years old and plan on retiring at age 65. I spend $4 each day on my favorite coffee like beverage at Starbucks. If I forego my daily Starbucks and can instead invest my money at a return rate of 10%, how much extra money will I have at the time of my retirement?

Answer 1

The $4 saved daily is an annuity. The daily interest is
0.10/365. The number of years for savings is 37 and the
number of days is 37*365 = 13505 days. FV of the annutiy
with daily compounding is to be found out.
FV of the annuity at t13505 [Extra money at the time of
retirement], using the formula for finding FV of annuity
=4*((1+0.10/365)^13505-1)/(0.10/365) =	$     575,631.46
Note:
It is assumed that the savings are made at the end of each day.
That is, it is an ordinary annuity.
If the savings are made at the beginning of each day, it would
be an annuity due and the total amount on retirrement would be:
=4*((1+0.10/365)^13505-1)*(1+0.10/365)/(0.10/365) =	$     575,789.17