Question

In: Finance

Tabitha saved $5,000 a year for ten years ($50,000) beginning at age 22 Tonya saved $10,000...

Tabitha saved $5,000 a year for ten years ($50,000) beginning at age 22 Tonya saved $10,000 a year for ten years ($100,000) beginning at age 40 Both made the same investments and realized a compound return of 6% annually Who has more money at age 67?

Solutions

Expert Solution

Tabitha:

  1. Find the FV of the annual PMTs at the end of 10 years
    • We are given the following information
    • PMT $              5,000.00
      r 6.00%
      n 10
      T 1
    • We need to solve the following equation to arrive at the required FV
    • So the FV is $65903.97
  2. Now we compound this for 67-32= 35 years
    • We are given the following information
    • PV $            65,903.97
      r 6.00%
      n 35
      frequency 1
    • We need to solve the following equation to arrive at the required FV
    • So the FV is $5,06,543.67

Tonya:

  1. Find the FV of the annual PMTs at the end of 10 years
    • We are given the following information
    • PMT $            10,000.00
      r 6.00%
      n 10
      T 1
    • We need to solve the following equation to arrive at the required FV
    • So the FV is $1,31,807.95
  2. Now we compound this for 67-50= 17 years
    • We are given the following information
    • PV $        1,31,807.95
      r 6.00%
      n 17
      frequency 1
    • We need to solve the following equation to arrive at the required FV
    • So the FV is $ 3,54,928.86

So Tabitha will have higher amount by the age of 67


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