Question

$20, 000 is deposited into an account earning 2% effective annual interest. At the end of each year, the interest earned in that year plus an additional $500 is withdrawn from this account and put into another account earning 5% effective annual interest. Find the accumulated value in the second account after 40 years (when the first account is completely depleted.)

Answer 1

Year	Opening balance	Interest	Closing balance	Deposit
1	-	-	-	500.00
2	500.00	10.00	510.00	500.00
3	1,010.00	20.20	1,030.20	500.00
4	1,530.20	30.60	1,560.80	500.00
5	2,060.80	41.22	2,102.02	500.00
6	2,602.02	52.04	2,654.06	500.00
7	3,154.06	63.08	3,217.14	500.00
8	3,717.14	74.34	3,791.48	500.00
9	4,291.48	85.83	4,377.31	500.00
10	4,877.31	97.55	4,974.86	500.00
11	5,474.86	109.50	5,584.36	500.00
12	6,084.36	121.69	6,206.04	500.00
13	6,706.04	134.12	6,840.17	500.00
14	7,340.17	146.80	7,486.97	500.00
15	7,986.97	159.74	8,146.71	500.00
16	8,646.71	172.93	8,819.64	500.00
17	9,319.64	186.39	9,506.04	500.00
18	10,006.04	200.12	10,206.16	500.00
19	10,706.16	214.12	10,920.28	500.00
20	11,420.28	228.41	11,648.68	500.00
21	12,148.68	242.97	12,391.66	500.00
22	12,891.66	257.83	13,149.49	500.00
23	13,649.49	272.99	13,922.48	500.00
24	14,422.48	288.45	14,710.93	500.00
25	15,210.93	304.22	15,515.15	500.00
26	16,015.15	320.30	16,335.45	500.00
27	16,835.45	336.71	17,172.16	500.00
28	17,672.16	353.44	18,025.61	500.00
29	18,525.61	370.51	18,896.12	500.00
30	19,396.12	387.92	19,784.04	500.00
31	20,284.04	405.68	20,689.72	500.00
32	21,189.72	423.79	21,613.51	500.00
33	22,113.51	442.27	22,555.79	500.00
34	23,055.79	461.12	23,516.90	500.00
35	24,016.90	480.34	24,497.24	500.00
36	24,997.24	499.94	25,497.18	500.00
37	25,997.18	519.94	26,517.13	500.00
38	27,017.13	540.34	27,557.47	500.00
39	28,057.47	561.15	28,618.62	500.00
40	29,118.62	582.37	29,700.99	500.00

Closing balance at end of year = 29700.99