Question

José is considering two different savings plans. With the first, you will have to deposit RD $ 500 every six months, and you will receive an interest rate of 7% per year capitalized each semester. With the second plan, you will have to deposit 1,000 RD $ each year with an interest rate of 7.5% capitalized annually. The initial deposit with Plan 1 is made within six months and with Plan 2 within 1 year. What is the future (terminal) value of each plan at the end of 10 years? What plan should Jose use assuming his only concern is the value of his savings at the end of 10 years? Would your answer change if the interest rate on the second plan was 7%?

Answer 1

The 7% per annum on the first plan is equivalent of 3.5% per six months since it is capitalized every six months.

Let's see the table below for the comparison.

		Amount deposited	Future value
		amount * (1+3.5%)^20-time(half years))	amount * (1+7.5%)^10-time(year))	amount * (1+7%)^10-time(year))
Time (years)	Time (half years)	7% p.a. capitalized six monthly	7.5% p.a. capitalized yearly	7% p.a. capitalized yearly	7% p.a. capitalized six monthly	7.5% p.a. capitalized yearly	7% p.a. capitalized yearly
1	1	500	1000	1000	961.25	1,838.46	1,917.24
2	2	500	1000	1000	928.74	1,718.19	1,783.48
3	3	500	1000	1000	897.34	1,605.78	1,659.05
4	4	500	1000	1000	866.99	1,500.73	1,543.30
5	5	500	1000	1000	837.67	1,402.55	1,435.63
6	6	500	1000	1000	809.35	1,310.80	1,335.47
7	7	500	1000	1000	781.98	1,225.04	1,242.30
8	8	500	1000	1000	755.53	1,144.90	1,155.63
9	9	500	1000	1000	729.98	1,070.00	1,075.00
10	10	500	1000	1000	705.30	1,000.00	1,000.00
	11	500			681.45
	12	500			658.40
	13	500			636.14
	14	500			614.63
	15	500			593.84
	16	500			573.76
	17	500			554.36
	18	500			535.61
	19	500			517.50
	20	500			500.00
				Future value	14,139.84	13,816.45	14,147.09