Question

Mr. Abebe deposited to a trust company a certain amount of money during the 40th birthday of his father. Five years later, he decided to start giving ten deposits of 6,000 birr each year. On the 55th birthday of his father he withdraws 50,000 birr for celebration. Interest at the rate of 15% per annum was to be paid on all amounts on deposit. There is a provision that his father could take 8,000 birr each year for ten years starting on the 61st birthday. How much did Mr. Abebe deposited during the 40th birthday of his father?

Answer 1

Let money deposited on 40th birthday is X birr

From his father's age between 46-55, there is deposit of 6,000 birr each year

On 55th birthday, 50,000 birr is withdrawed

His father withdraw 8,000 birr each year between age 61-70

Interest rate = 15% per year

I will calculate present value of all cash flow in at 40th birthday where present value is calculated as: [Cash Flow in any year / (1 + Rate of Interest)^^{(Current year - 40)}]

In the table below, values highlighted in green are deposits and red shows withdrawal.

Year	Cash Flow	Present value of cash flow at 40th birthday
45	6,000	2,983.06
46	6,000	2,593.97
47	6,000	2,255.62
48	6,000	1,961.41
49	6,000	1,705.57
50	6,000	1,483.11
51	6,000	1,289.66
52	6,000	1,121.44
53	6,000	975.17
54	6,000	847.97
55	-50,000	-                                                             6,144.72
61	-8,000	-                                                                425.05
62	-8,000	-                                                                369.60
63	-8,000	-                                                                321.40
64	-8,000	-                                                                279.47
65	-8,000	-                                                                243.02
66	-8,000	-                                                                211.32
67	-8,000	-                                                                183.76
68	-8,000	-                                                                159.79
69	-8,000	-                                                                138.95
70	-8,000	-                                                                120.82
		8,619.07

As net cash flows (all positive present value - all negative present value) is 8,619.07, deposit at the age of 40 must be 8,619.07