Emily Dorsey\'s current salary is $73,000 per year, and she is planning to retir
ID: 2820195 • Letter: E
Question
Emily Dorsey's current salary is $73,000 per year, and she is planning to retire 20 years from now. She anticipates that her annual salary will increase by $2,000 each year ($73,000 the first year, to S75,000 the second year, $77,000 the third year, and so forth), and she plans to deposit 5% of her yearly salary into a retirement fund that eams 7% interest compounded daily. What will be the amount of interest accumulated at the time of Emily's retirement? Assume 365 days per year. The amount of interest accumulated at the time of Emily's retirement will be $ 45457 thousand. (Round to the nearest whole number.)Explanation / Answer
Number of period n for year 1 = 19 x 365 = 6,935
Number of period n for year 2 = 18 x 365 = 6,570
Number of period n for year 3 = 17 x 365 = 6,205
Number of period n for year 4 = 18 x 365 = 5,840 and so on …
Year
Salary
Cash Deposited(C)
No. of Periods (n)
FV Factor Calculation
FV Factor (F)
FV (= C x F)
1
$ 73,000
$ 3,650
6,935
(1+0.07/365)^6935
3.780561267
$ 13,799.05
2
$ 75,000
$ 3,750
6,570
(1+0.07/365)^6570
3.524995619
$ 13,218.73
3
$ 77,000
$ 3,850
6,205
(1+0.07/365)^ 6205
3.286706189
$ 12,653.82
4
$ 79,000
$ 3,950
5,840
(1+0.07/365)^ 5840
3.064525106
$ 12,104.87
5
$ 81,000
$ 4,050
5,475
(1+0.07/365)^ 5475
2.857363447
$ 11,572.32
6
$ 83,000
$ 4,150
5,110
(1+0.07/365)^ 5110
2.6642059
$ 11,056.45
7
$ 85,000
$ 4,250
4,745
(1+0.07/365)^ 4745
2.484105788
$ 10,557.45
8
$ 87,000
$ 4,350
4,380
(1+0.07/365)^ 4380
2.31618043
$ 10,075.38
9
$ 89,000
$ 4,450
4,015
(1+0.07/365)^ 4015
2.159606812
$ 9,610.25
10
$ 91,000
$ 4,550
3,650
(1+0.07/365)^ 3650
2.01361756
$ 9,161.96
11
$ 93,000
$ 4,650
3,285
(1+0.07/365)^ 3285
1.877497169
$ 8,730.36
12
$ 95,000
$ 4,750
2,920
(1+0.07/365)^ 2920
1.750578506
$ 8,315.25
13
$ 97,000
$ 4,850
2,555
(1+0.07/365)^ 2555
1.632239535
$ 7,916.36
14
$ 99,000
$ 4,950
2,190
(1+0.07/365)^ 2190
1.521900269
$ 7,533.41
15
$ 101,000
$ 5,050
1,825
(1+0.07/365)^ 1825
1.419019929
$ 7,166.05
16
$ 103,000
$ 5,150
1,460
(1+0.07/365)^ 1460
1.323094292
$ 6,813.94
17
$ 105,000
$ 5,250
1,095
(1+0.07/365)^ 1095
1.233653221
$ 6,476.68
18
$ 107,000
$ 5,350
7,30
(1+0.07/365)^ 730
1.150258359
$ 6,153.88
19
$ 109,000
$ 5,450
3,65
(1+0.07/365)^365
1.072500983
$ 5,845.13
20
$ 111,000
$ 5,550
0
(1+0.07/365)^0
1
$ 5,550.00
Total savings
$ 92,000
Total FV
$ 184,311.35
Total interest earned = Total FV – total savings = $ 184,311.35 - $ 92,000 = $ 92,311.35
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