Question

Charlie wants to retire in 15 years, and he wants to have an annuity of $40,000 a year for 20 years after retirement. Charlie wants to receive the first annuity payment at the end of the year during his retirement period. Using an interest rate of 5% for both savings and retirement periods, how much must Charlie invest today in order to have his retirement annuity? (Round your answer to the nearest dollar).

Answer 1

Charlie must invest today $ 187,875

Step-1:Present value of annuity 15 years from today
Present value		=	Annuity	*	Present value of annuity of 1 for 20 years
		=	$           40,000	*	12.46221
		=	$       4,98,488
Working:
Present value of annuity of 1 for 15 years		=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.05)^-20)/0.05		i	5%
		=	12.46221034		n	20
Step-2:Investment amount today
Investment amount today		=	Value of annuity in 15 years	*	Present value of 1 received in 15 years
		=	$       4,98,488	*	0.376889
		=	$       1,87,875
Working:
Present value of 1 received in 15 years		=	(1+i)^-n		Where,
		=	(1+0.05)^-20		i	5%
		=	0.376889483		n	20