Today is your 20th birthday, and your parents just gave you $5,000 that you plan to use to open a stock brokerage account. You plan to add $500 to the account each year on your birthday. Your first $500 contribution will come one year from now on your 21st birthday. Your 45th and final $500 contribution will occur on your 65th birthday. You plan to withdraw $5,000 from the account five years from now on your 25th birthday to take a trip to Europe. You also anticipate that you will need to withdraw $10,000 from the account 10 years from now on your 30th birthday to take a trip to Asia. You expect that the account will have an average annual return of 12%. How much money do you anticipate that you will have in the account on your 65th birthday, following your final contribution

You anticipate that you will have $432,522 in the account on your 65th birthday, following your final contribution.

Explanation:

To calculate this, we use the formula for calculating the future value (FV) and FV of ordinary annuity as appropriate as given below:

FVd = D * (1 + r) ^n ... (1)

FVo = P * {[ (1 + r) ^n - 1] : r} ... (2)

Where,

FVd = Future value of initial deposit or balance amount as the case may be = ?

FVo = FV of ordinary annuity starting from a particular year = ?

D = Initial deposit = $5,000

P = Annual deposit = s $500

r = Average annual return = 12%, or 0.12

n = number years = to be determined as necessary

a) FV in five years from now

n = 5 for FVd

n = 4 for FVo

Substituting the values into equations (1) and (2), we have:

FVd = $5,000 * (1 + 0.12) ^5 = $8,812

FVo = $500 * {[ (1 + 0.12) ^4 - 1] : 0.12} = $2,390

FV5 = Total FV five years from now = $8,812 + $2,390 = $11,201

FVB5 = Balance after $5,000 withdrawal in year 5 = $11,201 - $5,000 = $6,201.

b) FV in 10 years from now

n = 10 - 5 = 5 for both FVd and FVo

Using equations (1) and (2), we have:

FV of FVB5 = $6,201 * (1 + 0.12) ^5 = $10,928

FVo = $500 * {[ (1 + 0.12) ^5 - 1] : 0.12} = $3,176

FV10 = Total FV 10 years from now = $10,928 + $3,176 = $14,104

FVB10 = Balance after $10,000 withdrawal in year 10 = $14,104 - $10,000 = $4,104

c) FV in 45 years from now

n = 45 - 10 = 35 for both FVd and FVo

Using equations (1) and (2), we have:

FV of FVB10 = $4,104 * (1 + 0.12) ^35 = $216,690

FVo = $500 * {[ (1 + 0.12) ^35 - 1] : 0.12} = $215,832

FV45 = Total FV 45 years from now = $216,690 + $215,832 = $432,522

Conclusion

Therefore, you anticipate that you will have $432,522 in the account on your 65th birthday, following your final contribution.