Question

Dawn and Mildred had the same starting sum of $120,000. Each made withdrawals of $24,000 a year. In years 2, 3, and 4, each had returns of 9% a year. Dawn had a 50% drop in year 1 and a 50% gain in year 5, while Mildred had a 50% gain in year 1 and a 50% drop in year 5.

A) Calculate the remaining sum for each woman at the end of year 5.

B) Explain why there is such a big difference in the remaining amounts.

Answer 1

Answer: Initial Investment : $120,000

Cash flow for Dawn :

Year 0 : $120,000

50% drop in first year and 9% growth in 2,3 and 4 years

Year 1 : 120000(1-0.5) - $24000 = $36000

Year 2 : 36000*(1+0.09) -$24000 = $15240

Year 3 : 15240*(1+0.09) -$24000 = -$7,388.4

So Dawn wont have money left to withdraw after year 3

Cash flow for Mildred :

Year 0 : $120,000

50% gain in first year and 9% growth in 2,3 and 4 years

Year 1 : 120000(1+0.5) - $24000 = $156000

Year 2 : 156000*(1+0.09) -$24000 = $146,040

Year 3 : 146,040*(1+0.09) -$24000 = $135183.6

Year 4: 135183.6 *(1+0.09) - $24000 = $123350.1

50% drop in 5th year

Year 5 : 123,350.1 (1-0.5) -$24000 = $37,675.06

Remaining Sum for Mildred at the end of 5th year = $37,675.06

Answer B: It shows the power of compounding, Dawn because of initial drop doesn't have much money to compound and grow on the other hand Mildred because of gain have sufficient amount to grow (compound) and take out $24000 as well from that.