Question

Please show formulas used. You're planning to save for his retirement 34 years from now. You plan to invest $4,200 per year for the first 7 years, $6,900 per year for the next 11 years, and $14,500 per year for the following 16 years. You make all investments at the end of each year. The investments will earn an annual rate of return of 9.7%. What will your investment be worth 34 years from now?

Answer 1

Step-1:Value of investment of first 7 years at the end of 34 years from now
Future value		=	Annual cash flow	*	Future value of annuity of 1 for 7 years	*	Future value of 1 for 27 years
		=	$          4,200.00	*	9.400178614	*	12.17808342
		=	$    4,80,799.87
Working:
Future value of annuity of 1		=	(((1+i)^n)-1)/i		Where,
		=	(((1+0.097)^7)-1)/0.097		i	=	9.70%
		=	9.400178614		n	=	7
Future value of 1 for 27 years		=	(1+i)^n		Where,
		=	(1+0.097)^27		i	=	9.70%
		=	12.17808342		n	=	27
Step-2:Value of investment of next 11 years at the end of 34 years from now
Future value		=	Annual cash flow	*	Future value of annuity of 1 for 11 years	*	Future value of 1 for 16 years
		=	$          6,900.00	*	18.23382362	*	4.398514634
		=	$    5,53,392.01
Working:
Future value of annuity of 1		=	(((1+i)^n)-1)/i		Where,
		=	(((1+0.097)^11)-1)/0.097		i	=	9.70%
		=	18.23382362		n	=	11
Future value of 1 for 27 years		=	(1+i)^n		Where,
		=	(1+0.097)^16		i	=	9.70%
		=	4.398514634		n	=	16
Step-3:Value of investment of next 16 years at the end of 34 years from now
Future value		=	Annual cash flow	*	Future value of annuity of 1 for 11 years
		=	$       14,500.00	*	35.03623334
		=	$    5,08,025.38
Working:
Future value of annuity of 1		=	(((1+i)^n)-1)/i		Where,
		=	(((1+0.097)^16)-1)/0.097		i	=	9.70%
		=	35.03623334		n	=	16
Step-4:Value of investment 34 years from now
Investment worth 34 years from now		=	$    4,80,799.87	+	$ 5,53,392.01	+	$ 5,08,025.38
		=	$ 15,42,217.26