Please show all work step by step You want to save enough money to retire

ID: 2784556 • Letter: #

Question

**Please show all work step by step** You want to save enough money to retire as a millionaire. (Age now is 25)

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?

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?

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?

d. What type of a problem is this?

a. Future value of annuity calculation:

required amount at the age of 65= 1000000

periodic payament= P

effective interest rate per annum (i)= %

number of periods (n) = 65-25= 40

Future value of annuity= P* [ (1+r)^n -1 ]/r

1000000= p* [ (1+0.1)^40 -1]/ 0.1 = p* 442.5926

P= 1 000 000/ 442.5926= 2259.41

by depositing every year 2259.41 for 40 years by the age of 65 1M will be received

b. All the same interest per month= 10%/12= 0.83333 and number of periods= 40*12= 480

1000000 = P* [(1+0.0083333)^480 -1]/0.0083333 = P*6324.08

P= 158

Monthly 158 should be set aside to earn 1M by the age of 65

c. per month interest= 11%/12= 0.91667%

1000000= P *[(1+0.009167)^480 -1]/ 0.0091667

P= 116

monthly deposit should by 116

d. It is future value of annuity calculation

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