Question

In: Economics

In the following table, assume that someone retires in 2006 with an initial income payment of...

In the following table, assume that someone retires in 2006 with an initial income payment of $25,000 per year in benefits. The benefit payment is then indexed to the Consumer Price Index (CPI) for the next 20 years. Assume also that the CPI would rise by 2% per year. Column (1) shows the value of the CPI in each year, using 2006 as the base year. Calculate the indexed nominal benefits by 2% per year in column (2), the real annual benefits in column (3), the indexed nominal benefits by 3% per year in column (4), and the real annual benefits in column (5).

Benefits of Indexed to CPI (rising to 2%)

Benefits of Indexed to CPI (rising to 3%)

Year

(1)

Price Index 2010 = 100

(2)

Nominal Annual Benefit (indexed at 2% per year)

(3)

Real Annual Benefit

(4)

Nominal Annual Benefit (indexed at 2% per year)

(5)

Real Annual Benefit

2006

2007

2008

2009

.......

2026

100.00

102.00

104.04

106.12

148.59

SR25000

Expert Solution

The first column indicates the rise in price level which is 2% per year.
The nominal income would rise by the price level if it is indexed at 2%

Year 2006 = 25000

Year 2007,
Price Level = 100 * 1.02 = 102
Nominal Income = 25000 * 1.02 = 25500
Real income is adjusted for the change in price level
(100 * 25500) / 102 = 25000

If the nominal income is indexed at 3%

Year 2007
Price level = 100 * 1.02 = 102
Nominal Income = 25000 * 1.03 = 25750
Real income is adjusted for change in price level
(100 * 25750) / 102 = 25245.10

So we can create a table for the values

Year	CPI	Nominal @ 2%	Real Benefits	Nominal @ 3%	Real Benefits
2006	100	25000.00	25000	25000	25000
2007	102.00	25500.00	25000	25750.00	25245.10
2008	104.04	26010.00	25000	26522.50	25492.60
2009	106.12	26530.20	25000	27318.18	25742.53
2010	108.24	27060.80	25000	28137.72	25994.90
2011	110.41	27602.02	25000	28981.85	26249.76
2012	112.62	28154.06	25000	29851.31	26507.11
2013	114.87	28717.14	25000	30746.85	26766.98
2014	117.17	29291.48	25000	31669.25	27029.40
2015	119.51	29877.31	25000	32619.33	27294.40
2016	121.90	30474.86	25000	33597.91	27561.99
2017	124.34	31084.36	25000	34605.85	27832.20
2018	126.82	31706.04	25000	35644.02	28105.07
2019	129.36	32340.17	25000	36713.34	28380.61
2020	131.95	32986.97	25000	37814.74	28658.85
2021	134.59	33646.71	25000	38949.19	28939.82
2022	137.28	34319.64	25000	40117.66	29223.54
2023	140.02	35006.04	25000	41321.19	29510.05
2024	142.82	35706.16	25000	42560.83	29799.36
2025	145.68	36420.28	25000	43837.65	30091.51
2026	148.59	37148.68	25000	45152.78	30386.53

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