Question

Which of the following will have the highest value after 20 years, assuming the same annual interest rate of 10%?

	A.	$170,000 deposited after 5 years
	B.	$110,000 deposited now
	C.	$20,000 deposits per year for 8 years, starting from now
	D.	10 yearly deposits from now that grows at 12% per year, with $10,000 as the first deposit (i.e., 10,000 now, 11,200 in a year, 12,544 in 2 years, etc.)

Answer 1

C.	$20,000 deposits per year for 8 years, starting from now has the highest value after 20 years

Working:

A.	Value after 20 years		=	170000*(1+0.10)^15		=	$ 7,10,132.19
B.	Value after 20 years		=	110000*(1+0.10)^20		=	$ 7,40,024.99
C.
	# 1
	Value after 7 years from now		=	Annuity*Future Value of annuity of 1
			=	$     20,000.00	*	12.57947691
			=	$ 2,51,589.54
	Future value of annuity of 1			=	((((1+i)^n)-1)/i)*(1+i)
				=	((((1+0.10)^8)-1)/0.10)*(1+0.10)
				=	12.57948
	# 2
	Value after 20 years		=	$ 2,51,589.54	*(1+0.10)^13
			=	$ 8,68,555.32
D.
Deposit number	Year	Cash flows		Future Value of 1		Future Value of cash flows
	a	b		c=1.10^(20-a)		d=b*c
1	0	$ 10,000.00		6.727499949		$     67,275.00
2	1	$ 11,200.00		6.115909045		$     68,498.18
3	2	$ 12,544.00		5.559917313		$     69,743.60
4	3	$ 14,049.28		5.054470285		$     71,011.67
5	4	$ 15,735.19		4.594972986		$     72,302.79
6	5	$ 17,623.42		4.177248169		$     73,617.39
7	6	$ 19,738.23		3.797498336		$     74,955.88
8	7	$ 22,106.81		3.452271214		$     76,318.72
9	8	$ 24,759.63		3.138428377		$     77,706.33
10	9	$ 27,730.79		2.853116706		$     79,119.17
Total						$ 7,30,548.73