Question

You currently have $55,000 in your retirement account.  You will make deposits of $11,000/year into your account for the next 20 years.  If the account earns 8% compounded quarterly, calculate how much you have in your account when you retire in 20 years.

Answer 1

Accumulated value in 20 years $ 785,299.63

Step-1:Calculation of annual effective interest rate
Annual effective interest rate	=	((1+(i/n))^n)-1		Where,
	=	((1+(0.08/4))^4)-1		i	=	8%
	=	8.24%		n	=	4
Step-2:Future value of current investment
Future value	=	P*(1+i)^n		Where,
	=	55000*(1+0.0824)^20		P	=	$ 55,000.00
	=	$ 2,68,149.15		i	=	8.24%
				n	=	20
Step-2:Future value of annual deposit
Future value of annual deposit	=	Annual deposit	*	Future value of annuity of 1
	=	$     11,000.00	*	47.01367957
	=	$ 5,17,150.48
Working:
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.0824)^20)-1)/0.0824		i	=	8.24%
	=	47.01367957		n	=	20
Step-3:Total accumulated value of money in 20 years
Accumulated value in 20 years	=	$ 2,68,149.15	+	$ 5,17,150.48
	=	$ 7,85,299.63
Note:
Any intermediary calculation has not been rounded off.
Annual effective interest rate has not been rounded off to 8.24%.