Use financial calculator to answer the question a. You are saving for your retirement. You have...

Use financial calculator to answer the question

a. You are saving for your retirement. You have decided that one year from today you will deposit 4 percent of your annual salary in an account which will earn 8 percent per year. Your salary currently (today) is $70,000, and it will increase at 2 percent per year throughout your career. How much money will you have for your retirement, which will begin in 35 years? Assume your first payment into the account is one year from today after your first increase.

$41,161.55
$71,400.00
$608,439.83
$809,528.99
$909,845.87

b. Pamela has received a job offer from a large investment bank as an assistant to the vice president. Her base salary will be $60,000 today. Assuming for simplicity that she will receive her first annual salary payment with the appropriate increment one year from the day she begins to work. In addition, she will get an immediate $20,000 bonus for joining the company today. Her salary will grow at 3 percent each year. Each year she will receive a bonus equal to 5 percent of her salary. Pamela is expected to work for the next 40 years. What is the present value of the offer, if the discount rate is 8 percent?

$20,000.00
$61,800.00
$1,122,929.30
$1,602,929.95
$2,395,101.72

Expert Solution

a.

Year (n)	Salary after 2% increase per year (Sn)	Formula used	Deposit (4% of salary)	Future Value (FV) = Sn*(1+8%)^(35-n)	Formula used
0	$70,000
1	$71,400.00	S*(1+2%)^1	$2,856.00	$39,099.02	S*(1+8%)^34
2	$72,828.00	S*(1+2%)^2	$2,913.12	$36,926.85	S*(1+8%)^33
3	$74,284.56	S*(1+2%)^3	$2,971.38	$34,875.36	S*(1+8%)^32
4	$75,770.25	S*(1+2%)^4	$3,030.81	$32,937.84	S*(1+8%)^31
5	$77,285.66	S*(1+2%)^5	$3,091.43	$31,107.96	S*(1+8%)^30
6	$78,831.37	S*(1+2%)^6	$3,153.25	$29,379.74	S*(1+8%)^29
7	$80,408.00	S*(1+2%)^7	$3,216.32	$27,747.53	S*(1+8%)^28
8	$82,016.16	S*(1+2%)^8	$3,280.65	$26,206.00	S*(1+8%)^27
9	$83,656.48	S*(1+2%)^9	$3,346.26	$24,750.11	S*(1+8%)^26
10	$85,329.61	S*(1+2%)^10	$3,413.18	$23,375.11	S*(1+8%)^25
11	$87,036.20	S*(1+2%)^11	$3,481.45	$22,076.49	S*(1+8%)^24
12	$88,776.93	S*(1+2%)^12	$3,551.08	$20,850.02	S*(1+8%)^23
13	$90,552.46	S*(1+2%)^13	$3,622.10	$19,691.69	S*(1+8%)^22
14	$92,363.51	S*(1+2%)^14	$3,694.54	$18,597.70	S*(1+8%)^21
15	$94,210.78	S*(1+2%)^15	$3,768.43	$17,564.50	S*(1+8%)^20
16	$96,095.00	S*(1+2%)^16	$3,843.80	$16,588.69	S*(1+8%)^19
17	$98,016.90	S*(1+2%)^17	$3,920.68	$15,667.10	S*(1+8%)^18
18	$99,977.24	S*(1+2%)^18	$3,999.09	$14,796.70	S*(1+8%)^17
19	$101,976.78	S*(1+2%)^19	$4,079.07	$13,974.66	S*(1+8%)^16
20	$104,016.32	S*(1+2%)^20	$4,160.65	$13,198.29	S*(1+8%)^15
21	$106,096.64	S*(1+2%)^21	$4,243.87	$12,465.06	S*(1+8%)^14
22	$108,218.58	S*(1+2%)^22	$4,328.74	$11,772.55	S*(1+8%)^13
23	$110,382.95	S*(1+2%)^23	$4,415.32	$11,118.52	S*(1+8%)^12
24	$112,590.61	S*(1+2%)^24	$4,503.62	$10,500.83	S*(1+8%)^11
25	$114,842.42	S*(1+2%)^25	$4,593.70	$9,917.45	S*(1+8%)^10
26	$117,139.27	S*(1+2%)^26	$4,685.57	$9,366.48	S*(1+8%)^9
27	$119,482.05	S*(1+2%)^27	$4,779.28	$8,846.12	S*(1+8%)^8
28	$121,871.69	S*(1+2%)^28	$4,874.87	$8,354.67	S*(1+8%)^7
29	$124,309.13	S*(1+2%)^29	$4,972.37	$7,890.52	S*(1+8%)^6
30	$126,795.31	S*(1+2%)^30	$5,071.81	$7,452.16	S*(1+8%)^5
31	$129,331.22	S*(1+2%)^31	$5,173.25	$7,038.15	S*(1+8%)^4
32	$131,917.84	S*(1+2%)^32	$5,276.71	$6,647.14	S*(1+8%)^3
33	$134,556.20	S*(1+2%)^33	$5,382.25	$6,277.85	S*(1+8%)^2
34	$137,247.32	S*(1+2%)^34	$5,489.89	$5,929.08	S*(1+8%)^1
35	$139,992.27	S*(1+2%)^35	$5,599.69	$5,599.69	S*(1+8%)^0
Value of deposits at the time of retirement (sum of FVs)				$608,587.65

(Answer is slightly different; please check if it is correct as all the steps are followed correctly)

b.

Year (n)	Salary after 3% increase per year (Sn)	Formula used	Bonus (5% of salary from year 1 onwards)	Total Income (= salary + Bonus)	Present Value (PV) = Sn/(1+8%)^n	Formula used
0			$20,000.00	$20,000.00	$20,000.00	S/(1+8%)^0
1	$61,800.00	S*(1+3%)^1	$3,090.00	$64,890.00	$60,083.33	S/(1+8%)^1
2	$63,654.00	S*(1+3%)^2	$3,182.70	$66,836.70	$57,301.70	S/(1+8%)^2
3	$65,563.62	S*(1+3%)^3	$3,278.18	$68,841.80	$54,648.84	S/(1+8%)^3
4	$67,530.53	S*(1+3%)^4	$3,376.53	$70,907.06	$52,118.80	S/(1+8%)^4
5	$69,556.44	S*(1+3%)^5	$3,477.82	$73,034.27	$49,705.89	S/(1+8%)^5
6	$71,643.14	S*(1+3%)^6	$3,582.16	$75,225.29	$47,404.70	S/(1+8%)^6
7	$73,792.43	S*(1+3%)^7	$3,689.62	$77,482.05	$45,210.03	S/(1+8%)^7
8	$76,006.20	S*(1+3%)^8	$3,800.31	$79,806.52	$43,116.98	S/(1+8%)^8
9	$78,286.39	S*(1+3%)^9	$3,914.32	$82,200.71	$41,120.82	S/(1+8%)^9
10	$80,634.98	S*(1+3%)^10	$4,031.75	$84,666.73	$39,217.08	S/(1+8%)^10
11	$83,054.03	S*(1+3%)^11	$4,152.70	$87,206.73	$37,401.47	S/(1+8%)^11
12	$85,545.65	S*(1+3%)^12	$4,277.28	$89,822.94	$35,669.92	S/(1+8%)^12
13	$88,112.02	S*(1+3%)^13	$4,405.60	$92,517.62	$34,018.54	S/(1+8%)^13
14	$90,755.38	S*(1+3%)^14	$4,537.77	$95,293.15	$32,443.61	S/(1+8%)^14
15	$93,478.04	S*(1+3%)^15	$4,673.90	$98,151.95	$30,941.59	S/(1+8%)^15
16	$96,282.39	S*(1+3%)^16	$4,814.12	$101,096.51	$29,509.11	S/(1+8%)^16
17	$99,170.86	S*(1+3%)^17	$4,958.54	$104,129.40	$28,142.94	S/(1+8%)^17
18	$102,145.98	S*(1+3%)^18	$5,107.30	$107,253.28	$26,840.03	S/(1+8%)^18
19	$105,210.36	S*(1+3%)^19	$5,260.52	$110,470.88	$25,597.44	S/(1+8%)^19
20	$108,366.67	S*(1+3%)^20	$5,418.33	$113,785.01	$24,412.37	S/(1+8%)^20
21	$111,617.67	S*(1+3%)^21	$5,580.88	$117,198.56	$23,282.17	S/(1+8%)^21
22	$114,966.20	S*(1+3%)^22	$5,748.31	$120,714.51	$22,204.29	S/(1+8%)^22
23	$118,415.19	S*(1+3%)^23	$5,920.76	$124,335.95	$21,176.31	S/(1+8%)^23
24	$121,967.65	S*(1+3%)^24	$6,098.38	$128,066.03	$20,195.93	S/(1+8%)^24
25	$125,626.68	S*(1+3%)^25	$6,281.33	$131,908.01	$19,260.93	S/(1+8%)^25
26	$129,395.48	S*(1+3%)^26	$6,469.77	$135,865.25	$18,369.22	S/(1+8%)^26
27	$133,277.34	S*(1+3%)^27	$6,663.87	$139,941.21	$17,518.79	S/(1+8%)^27
28	$137,275.66	S*(1+3%)^28	$6,863.78	$144,139.44	$16,707.74	S/(1+8%)^28
29	$141,393.93	S*(1+3%)^29	$7,069.70	$148,463.63	$15,934.23	S/(1+8%)^29
30	$145,635.75	S*(1+3%)^30	$7,281.79	$152,917.54	$15,196.54	S/(1+8%)^30
31	$150,004.82	S*(1+3%)^31	$7,500.24	$157,505.06	$14,492.99	S/(1+8%)^31
32	$154,504.97	S*(1+3%)^32	$7,725.25	$162,230.21	$13,822.02	S/(1+8%)^32
33	$159,140.11	S*(1+3%)^33	$7,957.01	$167,097.12	$13,182.11	S/(1+8%)^33
34	$163,914.32	S*(1+3%)^34	$8,195.72	$172,110.03	$12,571.83	S/(1+8%)^34
35	$168,831.75	S*(1+3%)^35	$8,441.59	$177,273.33	$11,989.80	S/(1+8%)^35
36	$173,896.70	S*(1+3%)^36	$8,694.83	$182,591.53	$11,434.72	S/(1+8%)^36
37	$179,113.60	S*(1+3%)^37	$8,955.68	$188,069.28	$10,905.33	S/(1+8%)^37
38	$184,487.01	S*(1+3%)^38	$9,224.35	$193,711.36	$10,400.46	S/(1+8%)^38
39	$190,021.62	S*(1+3%)^39	$9,501.08	$199,522.70	$9,918.95	S/(1+8%)^39
40	$195,722.27	S*(1+3%)^40	$9,786.11	$205,508.38	$9,459.74	S/(1+8%)^40
NPV (sum of PVs)					$1,122,929.30

jeff jeffy answered 2 years ago

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