Question

You contribute $2,000 annually to a retirement account for seven years and stop making payments at the age of 45. Your twin brother (or sister . . . whichever applies) opens an account at age 45 and contributes $2,000 a year until retirement at age 65 (20 years). You both earn 9 percent on your investments. How much can each of you withdraw for 25 years (that is, ages 66 through 90) from the retirement accounts?

You can withdraw $
Your twin can withdraw $

Answer 1

Accumulated value formula:

the accumulated value of all 7 deposits at age of 45 is calculated below:

((1+i)" - 1 Accumulated value = Deposit X

Accumulated value = 2,000 x ((1+0.09) - 1 0.09

Accumulated value = 2,000 x 1.828039 - 1 0.09

Accumulated value = 2,000 x 9.20043

Accumulated value = 18,400.87

The value at age of 65 will be:

Accumulated value = 18,400.87 x (1 +0.09)20

Accumulated value = 18,400.87 x 5.604411

Accumulated value = 103, 126.03

The accumulated value that twin brother have at age of 65 is calculated below:

Accumulated value = 2,000 x (1 +0.09 20 -1 0.09

Accumulated value = 2,000 x 5.604411-1 0.09

Accumulated value = 2,000 x 51.16012

Accumulated value = 102, 320.2393

The formula to calculate withdraw amount is given below:

the withdraw amount that individual can have is calculated below:

11 -(1+i)-" Present value = Withdraw x

103, 126.03 = Withdraw x (1-(1+0.09) -25 0.09

103, 126.03 = Withdraw x '1-0.1159678 0.09

103, 126.03 = Withdraw x 9.82278

10,498.87 = Withdraw

The withdraw amount that twin brother can have is calculated below:

102,320.2393 = withdraw x 1-(1+0.09) - 25 0.09

102,320.2393 = withdraw x 9.82258

10,416.84 = Withdraw

The individual can withdraw 10,498.87 each year for 20 years.

The twin brother can withdraw 10,416.84 each year for 20 years.