Question

Assume that you contribute $260 per month to a retirement plan for 20 years. Then you are able to increase the contribution to $520 per month for another 30 years. Given a 7.2 percent interest rate, what is the value of your retirement plan after the 50 years?  

Answer 1

Value of plan after 50 years is $ 18,55,620.43

We can also say that question says that $ 260 per month is contributed for 50 years and additional $ 260 per month for next 30 years.
Step-1:Future value of $ 260 monthly contribution for 50 years
Future value	=	Monthly contribution	*	Future value of annuity of 1
	=	$              260.00	*	5867.776224
	=	$ 15,25,621.82
Working:
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.006)^600)-1)/0.006		i	=	7.2%/12	=	0.006
	=	5867.776224		n	=	50*12	=	600
Step-2:Future value of $ 260 monthly contribution for 30 years
Future value	=	Monthly contribution	*	Future value of annuity of 1
	=	$              260.00	*	1269.225442
	=	$    3,29,998.61
Working:
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.006)^360)-1)/0.006		i	=	7.2%/12	=	0.006
	=	1269.225442		n	=	30*12	=	360
Step-3:Calculation of future value after the 50 years
Future value after 50 years	=	$ 15,25,621.82	+	$ 3,29,998.61
	=	$ 18,55,620.43