Respuesta :
Answer:
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.
