Question

3 If Derek plans to deposit $10,558.00 into his retirement account on each birthday beginning with his 26th and the account earns 11.00%, how long will it take him to accumulate $2,814,980.00? Submit Answer format: Number: Round to: 2 decimal places. Derek decides that he needs $198,343.00 per year in retirement to cover his living expenses. Therefore, he wants to withdraw $198343.0 on each birthday from his 66th to his 86.00th. How much will he need in his retirement account on his 65th birthday? Assume a interest rate of 5.00%. Submit Answer format: Currency: Round to: 2 decimal places.

Answer 1

Answer 3 : In question number 3 take the assumption for 30 years and calculate the accumulated amount in the following manner:

Year	Compounded Interest rate	Accumulated Amount
30	(1.11)30 =22.89	22.89*10558 = 241672.62
29	(1.11)29 =20.62	20.62*10558 = 217705.96
28	(1.11)28 =18.58	18.58*10558 = 196167.64
27	(1.11)27 = 16.74	16.74*10558 = 176740.92
26	(1.11)26 = 15.08	15.08*10558 = 159214.64
25	(1.11)25 = 13.59	13.59*10558 = 143,483.22
24	(1.11)24 = 12.24	12.24*10558 = 129,229.92
23	(1.11)23 = 11.03	11.03*10558 = 116,454.74
22	(1.11)22 = 9.93	9.93*10558 = 104,840.94
21	(1.11)21 = 8.95	8.95*10558 = 94,494.10
20	(1.11)20 = 8.06	8.06*10558 = 85,097.48
19	(1.11)19 = 7.26	7.26*10558 = 76,651.08
18	(1.11)18 = 6.54	6.54*10558 = 69,049.32
17	(1.11)17 = 5.90	5.90*10558 = 62,292.20
16	(1.11)16 = 5.31	5.31*10558 =56,062.98
15	(1.11)15 = 4.78	4.78*10558 = 50,467.24
14	(1.11)14 = 4.31	4.31*10558 = 45,504.98
13	(1.11)13 = 3.88	3.88*10558 = 40,965.04
12	(1.11)12 = 3.50	3.50*10558 = 36,953.00
11	(1.11)11  = 3.15	3.15*10558 = 33,257.70
10	(1.11)10 = 2.84	2.84*10558 =29,984.72
09	(1.11)9  = 2.56	2.56*10558 = 27,028.48
08	(1.11)8 = 2.30	2.30*10558 = 24,283.40
07	(1.11)7 = 2.08	2.08*10558 = 21,960.64
06	(1.11)6 = 1.87	1.87*10558 = 19,743.46
05	(1.11)5 = 1.69	1.69*10558 = 17,843.02
04	(1.11)4 = 1.52	1.52*10558 = 16,048.16
03	(1.11)3 = 1.37	1.37*10558 = 14,464.46
02	(1.11)2 = 1.23	1.23*10558 = 12,986.34
01	(1.11)1  = 1.11	1.11*10558 = 11,719.38

Total accumulated balance after 30 years of investment at the end of 30th year will be 2,332,357.78.

At the end of 31st year the amount will be :

(2,332,357.78*1.11) + (10,558*1.11) = 2,588,917.14 + 11,719.38 = 2,600,636.52

At the end of 32nd year the amount will be :

(2,600,636.52*1.11) + (10,558*1.11) = 2,886,706.54 + 11,719.38 = 2,898.425.92

So the accumulated amount which is required is $2,814,980.00 and the amount at the end of 32nd year is more than the required accumulated balance which means that we do not have to invest the amount for the whole 32nd year.

So the time period for which the amount should be invested is in between 32 years and 33 years.

So the amount which will be invested at the beginning of the 32nd year will be $2,600,636.52 + $10,558 = $2,611,194.52. The amount of interest for the 32nd year will be $203,785.48 i.e. $2,814,980 - $2,611,194.52.

Period for such interest will be calculated as below:

2,611,194.52 * 11% * No. of months/12 = 203,785.48

No.of months * 23935.95 = 203,785.48

No. of months = 203,785.48/23,935.95

No. of months = 8.51

So the total time period will be 31 years and 8.51 months or 31.71 years (approximately)

Question 4 . To answer this question we have to do the reverse calculation to arrive at the principle amount:

like to arrive at the value of $198,343.00 on his 86th birthday we have to use the following formula:

Present value divided by (1.05)ⁿ. Here n represent the number of year form his 65th birthday. So on 86th Birthday the value of n will be 21.

Years	Accumulated interest rate	Accumulated Amount required	Value of amount of 65th Birthday = Column3/Column2
21	(1.05)21 = 2.79	198,343	71,090.68
20	(1.05)20 = 2.65	198,343	74,846.42
19	(1.05)19 = 2.53	198,343	78,396.44
18	(1.05)18 = 2.41	198,343	82,300.00
17	(1.05)17 = 2.29	198,343	86,612.66
16	(1.05)16 = 2.18	198,343	90,983.03
15	(1.05)15 = 2.08	198,343	95,357.21
14	(1.05)14 = 1.98	198,343	100,173.23
13	(1.05)13 = 1.89	198,343	104,943.39
12	(1.05)12 = 1.80	198,343	110,190.56
11	(1.05)11 = 1.71	198,343	115,990.06
10	(1.05)10 = 1.63	198,343	121,682.82
09	(1.05)9 = 1.55	198,343	127,963.23
08	(1.05)8 = 1.48	198,343	134,015.54
07	(1.05)7 = 1.41	198,343	140,668.79
06	(1.05)6 = 1.34	198,343	148,017.16
05	(1.05)5 = 1.28	198,343	154,955.47
04	(1.05)4 = 1.22	198,343	162,576.23
03	(1.05)3 = 1.16	198,343	170,985.34
02	(1.05)2 = 1.10	198,343	180.311.82
01	(1.05)1 = 1.05	198,343	188,898.10

Total amount to be available on the 65th Birthday will be $  2,540,958.18