Question

Problem 10-7

Lindsay is 25 years old and has a new job in web development. She wants to make sure that she is financially sound in 30 years, so she plans to invest the same amount into a retirement account at the end of every year for the next 30 years.

(a)	Construct a data table in Excel that will show Lindsay the balance of her retirement account for various levels of annual investment and return. If Lindsay invests $11,000 at return of 6%, what would be the balance at the end of 20th year in the account?
	If required, round your answers to two decimal places.
	$
(b)	Develop the two-way table in Excel for the balance at the end of 30th year in the account. Consider annual investment amounts of $5000 to $20,000 in increments of $1000, and returns of 0% to 12% in increments of 1%. Note that because Lindsay invests at the end of the year, there is no interest earned on the contribution for the year in which she contributes. Complete the below table.
	If required, round your answers to two decimal places.
	3% 4% $5,000 $ $ $6,000 $ $ $7,000 $ $ $8,000 $ $ $9,000 $ $ $10,000 $ $ $11,000 $ $ $12,000 $ $ $13,000 $ $ $14,000 $ $ $15,000 $ $ $16,000 $ $ $17,000 $ $ $18,000 $ $ $19,000 $ $ $20,000 $ $

Answer 1

a. The balance at the end of 20th year in the account is the future value of annual deposits for 20 years

FV of deposits for 20 years = PMT [(1+i) ^n – 1] /i

Where,

Future value of deposits (FV) =?

Annual deposits PMT = $11,000

Number of deposits n = 20 annual deposits

Annual interest rate I =6%

Therefore          

FV = $11,000 * [(1+6%) ^20 -1]/6%

= $404,641.50

The balance at the end of 20th year in the account is $404,641.50.

b. Similarly we can use above formula to calculate in Excel for the balance at the end of 30th year in the account.

The annual investment amounts of $5000 to $20,000 in increments of $1000, and returns of 0% to 12% in increments of 1%.

Number of deposits n = 30 annual deposits

The balance at the end of 30th year in the account
Period of deposit (years) n =		30
	Annual Interest rate
Annual Investment	0%	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%	11%	12%
$5,000	$150,000.00	$173,924.46	$202,840.40	$237,877.08	$280,424.69	$332,194.24	$395,290.93	$472,303.93	$566,416.06	$681,537.69	$822,470.11	$995,104.39	$1,206,663.42
$6,000	$180,000.00	$208,709.35	$243,408.48	$285,452.49	$336,509.63	$398,633.09	$474,349.12	$566,764.72	$679,699.27	$817,845.23	$986,964.14	$1,194,125.27	$1,447,996.11
$7,000	$210,000.00	$243,494.24	$283,976.55	$333,027.91	$392,594.56	$465,071.93	$553,407.30	$661,225.50	$792,982.48	$954,152.77	$1,151,458.16	$1,393,146.15	$1,689,328.79
$8,000	$240,000.00	$278,279.13	$324,544.63	$380,603.33	$448,679.50	$531,510.78	$632,465.49	$755,686.29	$906,265.69	$1,090,460.31	$1,315,952.18	$1,592,167.02	$1,930,661.47
$9,000	$270,000.00	$313,064.02	$365,112.71	$428,178.74	$504,764.44	$597,949.63	$711,523.68	$850,147.08	$1,019,548.90	$1,226,767.85	$1,480,446.20	$1,791,187.90	$2,171,994.16
$10,000	$300,000.00	$347,848.92	$405,680.79	$475,754.16	$560,849.38	$664,388.48	$790,581.86	$944,607.86	$1,132,832.11	$1,363,075.39	$1,644,940.23	$1,990,208.78	$2,413,326.84
$11,000	$330,000.00	$382,633.81	$446,248.87	$523,329.57	$616,934.32	$730,827.32	$869,640.05	$1,039,068.65	$1,246,115.32	$1,499,382.92	$1,809,434.25	$2,189,229.66	$2,654,659.53
$12,000	$360,000.00	$417,418.70	$486,816.95	$570,904.99	$673,019.25	$797,266.17	$948,698.23	$1,133,529.44	$1,359,398.53	$1,635,690.46	$1,973,928.27	$2,388,250.54	$2,895,992.21
$13,000	$390,000.00	$452,203.59	$527,385.03	$618,480.40	$729,104.19	$863,705.02	$1,027,756.42	$1,227,990.22	$1,472,681.74	$1,771,998.00	$2,138,422.29	$2,587,271.41	$3,137,324.90
$14,000	$420,000.00	$486,988.48	$567,953.11	$666,055.82	$785,189.13	$930,143.87	$1,106,814.61	$1,322,451.01	$1,585,964.96	$1,908,305.54	$2,302,916.32	$2,786,292.29	$3,378,657.58
$15,000	$450,000.00	$521,773.37	$608,521.19	$713,631.24	$841,274.07	$996,582.71	$1,185,872.79	$1,416,911.79	$1,699,248.17	$2,044,613.08	$2,467,410.34	$2,985,313.17	$3,619,990.27
$16,000	$480,000.00	$556,558.26	$649,089.27	$761,206.65	$897,359.00	$1,063,021.56	$1,264,930.98	$1,511,372.58	$1,812,531.38	$2,180,920.62	$2,631,904.36	$3,184,334.05	$3,861,322.95
$17,000	$510,000.00	$591,343.16	$689,657.35	$808,782.07	$953,443.94	$1,129,460.41	$1,343,989.17	$1,605,833.37	$1,925,814.59	$2,317,228.16	$2,796,398.39	$3,383,354.92	$4,102,655.63
$18,000	$540,000.00	$626,128.05	$730,225.43	$856,357.48	$1,009,528.88	$1,195,899.26	$1,423,047.35	$1,700,294.15	$2,039,097.80	$2,453,535.69	$2,960,892.41	$3,582,375.80	$4,343,988.32
$19,000	$570,000.00	$660,912.94	$770,793.50	$903,932.90	$1,065,613.82	$1,262,338.10	$1,502,105.54	$1,794,754.94	$2,152,381.01	$2,589,843.23	$3,125,386.43	$3,781,396.68	$4,585,321.00
$20,000	$600,000.00	$695,697.83	$811,361.58	$951,508.31	$1,121,698.76	$1,328,776.95	$1,581,163.72	$1,889,215.73	$2,265,664.22	$2,726,150.77	$3,289,880.45	$3,980,417.56	$4,826,653.69