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 At the end of each year, the interest earned in that year plus an additional $500 is withdrawn from this account and put into another account earning 5% effective annual interest.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

Step-1 (Calculation of Withdrawan from First account)

	A	A*2%=B	B+500 = C	A+B-C
Year	Opening balance	Interest@2% on opening blance	Withdrawn(Interest+$500) or deposit at 2nd account	Closing value
1	20000	400	900	19500
2	19500	390	890	19000
3	19000	380	880	18500
4	18500	370	870	18000
5	18000	360	860	17500
6	17500	350	850	17000
7	17000	340	840	16500
8	16500	330	830	16000
9	16000	320	820	15500
10	15500	310	810	15000
11	15000	300	800	14500
12	14500	290	790	14000
13	14000	280	780	13500
14	13500	270	770	13000
15	13000	260	760	12500
16	12500	250	750	12000
17	12000	240	740	11500
18	11500	230	730	11000
19	11000	220	720	10500
20	10500	210	710	10000
21	10000	200	700	9500
22	9500	190	690	9000
23	9000	180	680	8500
24	8500	170	670	8000
25	8000	160	660	7500
26	7500	150	650	7000
27	7000	140	640	6500
28	6500	130	630	6000
29	6000	120	620	5500
30	5500	110	610	5000
31	5000	100	600	4500
32	4500	90	590	4000
33	4000	80	580	3500
34	3500	70	570	3000
35	3000	60	560	2500
36	2500	50	550	2000
37	2000	40	540	1500
38	1500	30	530	1000
39	1000	20	520	500
40	500	10	510	0

Step-2(Calculation of accumulate balance on 2nd account)-

	A	A*5%=B	C	A+B+C
Year	Opening balance	interest@5% on opening balnce	Deposit from 1st account	Closing balance
1	0.00	0.00	900.00	900.00
2	900.00	45.00	890.00	1835.00
3	1835.00	91.75	880.00	2806.75
4	2806.75	140.34	870.00	3817.09
5	3817.09	190.85	860.00	4867.94
6	4867.94	243.40	850.00	5961.34
7	5961.34	298.07	840.00	7099.41
8	7099.41	354.97	830.00	8284.38
9	8284.38	414.22	820.00	9518.60
10	9518.60	475.93	810.00	10804.52
11	10804.52	540.23	800.00	12144.75
12	12144.75	607.24	790.00	13541.99
13	13541.99	677.10	780.00	14999.09
14	14999.09	749.95	770.00	16519.04
15	16519.04	825.95	760.00	18104.99
16	18104.99	905.25	750.00	19760.24
17	19760.24	988.01	740.00	21488.26
18	21488.26	1074.41	730.00	23292.67
19	23292.67	1164.63	720.00	25177.30
20	25177.30	1258.87	710.00	27146.17
21	27146.17	1357.31	700.00	29203.48
22	29203.48	1460.17	690.00	31353.65
23	31353.65	1567.68	680.00	33601.33
24	33601.33	1680.07	670.00	35951.40
25	35951.40	1797.57	660.00	38408.97
26	38408.97	1920.45	650.00	40979.42
27	40979.42	2048.97	640.00	43668.39
28	43668.39	2183.42	630.00	46481.81
29	46481.81	2324.09	620.00	49425.90
30	49425.90	2471.29	610.00	52507.19
31	52507.19	2625.36	600.00	55732.55
32	55732.55	2786.63	590.00	59109.18
33	59109.18	2955.46	580.00	62644.64
34	62644.64	3132.23	570.00	66346.87
35	66346.87	3317.34	560.00	70224.22
36	70224.22	3511.21	550.00	74285.43
37	74285.43	3714.27	540.00	78539.70
38	78539.70	3926.98	530.00	82996.68
39	82996.68	4149.83	520.00	87666.52
40	87666.52	4383.33	510.00	92559.84

Hence accumulated balance on 2 nd account after 40 year= $ 92559.84