Question

3. [20PTS] Mr. Lee deposited a large amount of money in his first bank account. Annual withdrawals of 30,000 pesos starting EOY 1 were made for 7 years to pay for personal expenses. He stopped withdrawing after the 7th year when he was assigned to work abroad. After 3 years of working abroad without withdrawing or depositing from his bank account, he went back to the Philippines. He started withdrawing money again on the 10th year with an amount of 5,000 pesos, 7,000 pesos on the 11th year, 9,000 pesos on the 12th year, and the same trend goes up to the 15th year. After which, the following withdrawals were made: 16th year 2,500 pesos 17th year 3,000 pesos 18th year 3,500 pesos 19th year 4,000 pesos 20th year 4,500 pesos. The bank uses a nominal interest rate of 5% compounded annually.(a) What should be the minimum initial investment to accommodate all the transactions he made?(b) If 500,000 pesos is the initial investment, how much money is left after 25 years?

Answer 1

Time	Amount	Discount factor	Present value = Amount* discount factor
1	30000	1/(1+5%)^1 = 0.9524	30000*0.9524 = 28572
2	30000	1/(1+5%)^2 = 0.9070	30000*0.9070 = 27210
3	30000	0.8638	25915.13
4	30000	0.8227	24681.07
5	30000	0.7835	23505.78
6	30000	0.7462	22386.46
7	30000	0.7107	21320.44
10	5000	0.6139	3069.57
11	7000	0.5847	4092.76
12	9000	0.5568	5011.54
13	9000	0.5303	4772.89
14	9000	0.5051	4545.61
15	9000	0.4810	4329.15
16	2500	0.4581	1145.28
17	3000	0.4363	1308.89
18	3500	0.4155	1454.32
19	4000	0.3957	1582.94
20	4500	0.3769	1696.00
Sum of all present values	206599.83

(a) Minimum initial investment = 206,599.83

(b) If initial investment = 500,000

Present value (t = 0) of money left = 500,000 - 206,599.83 = 293400.17

Future value (ie value at t = 25) = 293400.17 * (1 + 5%)^25 = 993,557.1 (money left after 25 years)