Question

Rates are 8% p.a. compounded semi-annually.

a. You are going to make 30 monthly deposits of $500 each into your bank account starting in exactly 1 month. How much will you have immediately after the last deposit?

b. You are going to make 30 monthly deposits of $500 each into your bank account starting in exactly 7 months. How much will you have immediately after the last deposit?

c. You made the first of 30 monthly deposits of $500 each into your bank account exactly 7 months ago. How much will you have immediately after the last deposit?

Answer 1

Given Interest rate is 8% per annum compounded semi annually

Let us calculate the monthly rate.

(1+X)^12 = 1.08

Hence X = 0.00643403 = 0.6434%

Let us make the investment schedules for all the 3 options.

a) Investment for 30months starting in 1 month.

Month	Initial Investment	Compounding Factor	Future Value
1	500	1.2044092	602.20
2	500	1.1967096	598.35
3	500	1.1890591	594.53
4	500	1.1814576	590.73
5	500	1.1739047	586.95
6	500	1.1664000	583.20
7	500	1.1589433	579.47
8	500	1.1515343	575.77
9	500	1.1441727	572.09
10	500	1.1368581	568.43
11	500	1.1295903	564.80
12	500	1.1223689	561.18
13	500	1.1151937	557.60
14	500	1.1080644	554.03
15	500	1.1009807	550.49
16	500	1.0939422	546.97
17	500	1.0869488	543.47
18	500	1.0800000	540.00
19	500	1.0730957	536.55
20	500	1.0662355	533.12
21	500	1.0594191	529.71
22	500	1.0526464	526.32
23	500	1.0459169	522.96
24	500	1.0392305	519.62
25	500	1.0325868	516.29
26	500	1.0259856	512.99
27	500	1.0194265	509.71
28	500	1.0129095	506.45
29	500	1.0064340	503.22
30	500	1.0000000	500.00
		Total Future Value	16,487.21

b) 500 deposited starting exactly after 7 months.

Month	Initial Investment	Compounding Factor	Future Value
1	0	1.2597120	-
2	0	1.2516588	-
3	0	1.2436571	-
4	0	1.2357065	-
5	0	1.2278067	-
6	0	1.2199575	-
7	0	1.2121584	-
8	500	1.2044092	602.20
9	500	1.1967096	598.35
10	500	1.1890591	594.53
11	500	1.1814576	590.73
12	500	1.1739047	586.95
13	500	1.1664000	583.20
14	500	1.1589433	579.47
15	500	1.1515343	575.77
16	500	1.1441727	572.09
17	500	1.1368581	568.43
18	500	1.1295903	564.80
19	500	1.1223689	561.18
20	500	1.1151937	557.60
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