Question

You deposit $5,000 into an account at the end of year 0. You deposit $5,000 every three
(3) months beginning at the end of year 1 and continuing through the end of year 3.
You also deposit into the account an amount X starting at the end of year 6 and repeat it
every three (3) months for a total of four (4) deposits. You withdraw $112,160 at the
end of year 7. After the withdrawal at the end of year 7, there is no more money in the
account. The account pays 4% compounded quarterly. What is the amount you must
every three (3) months deposit starting at the end of year 6 (value of X)?

Answer 1

The table below should help answer. 4% compounded quarterly can also be represented as 1% for each time period where each time period = 3 months.

We need to solve for x, for which see the second table below.

			amount deposited * (1.01^(28-time))
Year	Time (multiples of 3 months)	Amount deposited	Amount incl interest at t=28	Amount withdrawn
0	0	5,000	6,606
	1		-
	2		-
	3		-
1	4	5,000	6,349
	5	5,000	6,286
	6	5,000	6,224
	7	5,000	6,162
2	8	5,000	6,101
	9	5,000	6,041
	10	5,000	5,981
	11	5,000	5,922
3	12	5,000	5,863
	13		-
	14		-
	15		-
4	16		-
	17		-
	18		-
	19		-
5	20		-
	21		-
	22		-
	23		-
6	24	x
	25	x
	26	x
	27	x
7	28			112160

Table including value of x

			amount deposited * (1.01^(28-time))
Year	Time (multiples of 3 months)	Amount deposited	Amount incl interest at t=28	Amount withdrawn
0	0	5,000	6,606
	1		-
	2		-
	3		-
1	4	5,000	6,349
	5	5,000	6,286
	6	5,000	6,224
	7	5,000	6,162
2	8	5,000	6,101
	9	5,000	6,041
	10	5,000	5,981
	11	5,000	5,922
3	12	5,000	5,863
	13		-
	14		-
	15		-
4	16		-
	17		-
	18		-
	19		-
5	20		-
	21		-
	22		-
	23		-
6	24	12,345	12,846
	25	12,345	12,719
	26	12,345	12,593
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