Question

3.You want to save enough money to retire as a millionaire. (show all work please)

a. If you could earn 10% with common stocks, how much would you have to set aside per year to have $1,000,000 when you are 65? Please use your own age. (Im 21 now, so a 44 year difference)

b. If you were going to make deposit monthly, how much would you have to set aside per month to have $1,000,000 when you are 65? Please use your own age.

c. If you were able to earn 11%, how much would you have to set aside per month to have $1,000,000 when you are 65? Please use your own age.

d. What type of a problem is this? ___________

Answer 1

a)

Future value = Annuity *[(1 + r)ⁿ - 1] / r

1,000,000 = Annuity *[(1 + 0.1)⁴⁴ - 1] / 0.1

1,000,000 = Annuity * 652.64076

Annuity = $1,532.24

Annual payments will be $1,532.24

b)

Rate = 10% / 12 = 0.8333%

Number of periods = 44 * 12 = 528

Future value = Annuity *[(1 + r)ⁿ - 1] / r

1,000,000 = Annuity *[(1 + 0.0083333)⁵²⁸ - 1] / 0.0083333

1,000,000 = Annuity * 9,477.38673

Annuity = $105.51

Monthly payments will be $105.51

c)

Rate = 11% / 12 = 0.9167%

Number of periods = 44 * 12 = 528

Future value = Annuity *[(1 + r)ⁿ - 1] / r

1,000,000 = Annuity *[(1 + 0.009167)⁵²⁸ - 1] / 0.009167

1,000,000 = Annuity * 13,388.56349

Annuity = $74.69

Monthly payments will be $74.69

d)

This is an example of ordinary annuity