Question

Luis has $100,000 in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to "roll over" his assets to a new account. Luis also plans to put $3000/quarter into the new account until his retirement 20 years from now. If the new account earns interest at the rate of 4.5%/year compounded quarterly, how much will Luis have in his account at the time of his retirement? Hint: Use the compound interest formula and the annuity formula. (Round your answer to the nearest cent.)

Answer 1

Step-1:Calculation of future value of present fund in his retirement account
	Future Value of 1	=	(1+i)^n		Where,
		=	(1+0.01125)^80		i	4.5%/4	=	0.01125
		=	2.447275		n	20*4	=	80
	Future Value of $ 100,000	=	$                                       1,00,000	x	2.447274977
		=	$                                 2,44,727.50
Step-2:Calculation of future value of quarterly investment
	Future Value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
		=	(((1+0.01125)^80)-1)/0.01125		i	0.01125
		=	128.64666		n	80
	Future value of quarterly deposit	=	Quarterly deposit x Future value of annuity of 1
		=	$                                       3,000.00	x	128.64666
		=	$                                 3,85,939.99
Step-3:Calculation of future value of all investments
	Future Value of all investments	=	Step-1 Value + Step-2 Value
		=	$                                 2,44,727.50	+	$ 3,85,939.99
		=	$                                 6,30,667.49
Thus,
	Luis will have in his account at the time of his retirement		$  6,30,667.49