Answer:
Kimberly will have $27,632.90 while Kaitlyn will $188,921.57 at age 67.
Explanation:
The relevant formula to use here is the formula for the Future Value (FV) of an Annuity FVA.
The future value of an annuity refers to the value at a specific date in the future of an investment or payment that recur regularly over a certain period.
The formula for calculating FVA is as follws:
FV = M × {[(1 + r)^n - 1] ÷ r} ................................. (1)
Where,
FV = Future value of an annuity or investment stream
M = Amount of each annuity
r = Interest rate
n = number of periods the investment will be made
FV of Kimberly:
Since Kimberly will never sets aside another penny after 10 years, we have:
M = $2,000
r = 7% = 0.07
n = 10
Substituting the values for Kimberly into equation (1), we have:
Kimberly FV = 2,000 × {[(1 + 0.07)^10 - 1] ÷ 0.07}
= 2,000 × {[(1.07)^10 - 1] ÷ 0.07}
= 2,000 × {[1.96715135728957 - 1] ÷ 0.07}
= 2,000 × {0.96715135728957 ÷ 0.07}
= 2,000 × 13.8164479612795
Kimberly FV = $27,632.90
FV of Kaitlyn:
M = $2,000
r = 7% = 0.07
n = 30
Kaitlyn FV = 2,000 × {[(1 + 0.07)^30 - 1] ÷ 0.07}
= 2,000 × {[(1.07)^30 - 1] ÷ 0.07}
= 2,000 × {[7.61225504266203 - 1] ÷ 0.07}
= 2,000 × {6.61225504266203 ÷ 0.07}
= 2,000 × 94.4607863237433
Kaitlyn FV = $188,921.57
Therefore, Kimberly will have $27,632.90 while Kaitlyn will $188,921.57 at age 67.
