Question

17. From age 20 to 30 Jack invested $2,000 per year in his IRA, and never saved another penny in his life. From age 20 to 65, Jill invested $2,000 per year in her IRA. Who do you think will have more money when they reach retirement age of 65? (Show your work). Assume opportunity cost of capital is 10%.

Answer 1

as Jill saved the same amount of $2000 for 45 years and Jack saved only for 10 years , and the rate of interest earned by them was the same, Jill would have more money as compared to Jack when they reach retirement at the age of 65.

Jack's balance at the age of 30 = 2000*1.1^9 + 2000*1.1^8 +.....+2000

= 2000/0.1 * (1.1^10-1)

=$31874.85

Balance at the age of 65 = 31874.85 *1.1^35 = $895,760.96

Jill's balance at the age of 30 = 2000*1.1^44 + 2000*1.1^43 +.....+2000

= 2000/0.1 * (1.1^45-1)

=$1,437,809.67