Question

Having just started a nice job after graduation, you would like to be financially responsible and start planning for your expected retirement in 40 years. What will be the value of your Roth IRA be if you fund it with $2,000 each year and earn a 7% rate of return? Please provide a sensitivity analysis to explore the range of outcomes.

Answer 1

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                2,000.00
rate of interest per period	r=
Rate of interest per year		7.0000%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.07*12/12	7.0000%
Number of periods
Number of years		40
Number of payments in a year		1
Total number of periods	n=	40
FV of annuity	=	2000* [ (1+0.07)^40 -1]/0.07
FV of annuity	=	399,270.22

Future value is: $399,270.22

Range of outcomes by changing interest rate and annual contribution is:

Deposit	5%	5.50%	6.00%	6.50%	7.00%	7.50%	8.00%	8.50%	9.00%	9.50%
1500	$ 181,199.66	$ 204,908.42	$ 232,142.95	$ 263,447.87	$ 299,452.67	$ 340,884.78	$    388,584.78	$    443,523.80	$    506,823.67	$    579,779.99
1750	$ 211,399.60	$ 239,059.82	$ 270,833.44	$ 307,355.85	$ 349,361.45	$ 397,698.91	$    453,348.91	$    517,444.44	$    591,294.28	$    676,409.99
2000	$ 241,599.55	$ 273,211.23	$ 309,523.93	$ 351,263.83	$ 399,270.22	$ 454,513.04	$    518,113.04	$    591,365.07	$    675,764.89	$    773,039.98
2250	$ 271,799.49	$ 307,362.63	$ 348,214.42	$ 395,171.81	$ 449,179.00	$ 511,327.17	$    582,877.17	$    665,285.71	$    760,235.50	$    869,669.98
2500	$ 301,999.44	$ 341,514.04	$ 386,904.91	$ 439,079.79	$ 499,087.78	$ 568,141.30	$    647,641.30	$    739,206.34	$    844,706.11	$    966,299.98
2750	$ 332,199.38	$ 375,665.44	$ 425,595.41	$ 482,987.77	$ 548,996.56	$ 624,955.43	$    712,405.43	$    813,126.97	$    929,176.72	$ 1,062,929.98
3000	$ 362,399.32	$ 409,816.84	$ 464,285.90	$ 526,895.75	$ 598,905.34	$ 681,769.56	$    777,169.56	$    887,047.61	$ 1,013,647.34	$ 1,159,559.98
3250	$ 392,599.27	$ 443,968.25	$ 502,976.39	$ 570,803.73	$ 648,814.11	$ 738,583.69	$    841,933.69	$    960,968.24	$ 1,098,117.95	$ 1,256,189.97
3500	$ 422,799.21	$ 478,119.65	$ 541,666.88	$ 614,711.71	$ 698,722.89	$ 795,397.82	$    906,697.82	$ 1,034,888.88	$ 1,182,588.56	$ 1,352,819.97
3750	$ 452,999.15	$ 512,271.05	$ 580,357.37	$ 658,619.68	$ 748,631.67	$ 852,211.95	$    971,461.95	$ 1,108,809.51	$ 1,267,059.17	$ 1,449,449.97
4000	$ 483,199.10	$ 546,422.46	$ 619,047.86	$ 702,527.66	$ 798,540.45	$ 909,026.08	$ 1,036,226.07	$ 1,182,730.14	$ 1,351,529.78	$ 1,546,079.97

Please rate.