Beginning at age 27, Kimberly invests $2000 per year for ten years and then never sets aside another penny. Kaitlyn waits ten years and then invests $2000 per year for the next 30 years. Assuming they both earn 7 percent, how much will each twin have at age 67?

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.

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