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?

Expert Solution

Tabitha:

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
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:

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
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

jeff jeffy answered 7 months ago

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