Question

Which amount will be worth more in the future?

(1)    $300 invested monthly for 35 years with an average annual return of 10% compounded monthly.

or

(2)    $1,000,000 lottery you win 35 years from now

Note: You must support your response with a calculation!

Answer 1

(1)    $300 invested monthly for 35 years with an average annual return of 10% compounded monthly will be more worthy in the future.

			Future value
Option 1			$       11,38,874
Option 2			$       10,00,000
So, Option 1 has higher future worth.
Working:
Future value of annuity of 1		=	(((1+i)^n)-1)/i			Where,
		=	(((1+0.008333)^420)-1)/0.008333			i	10%/12	=	0.008333
		=	3796.246142			n	35*12	=	420
Future value of monthly deposit		=	Monthly deposit	*	Future value of annuity of 1
		=	$                   300	*	3796.246142
		=	$ 11,38,874