Earl E. Bird has decided to start saving for his retirement. Beginning on his twenty-first birthday
QUESTION
Earl E. Bird has decided to start saving for his retirement. Beginning on his twenty-first birthday, Earl plans to invest $2,000 each birthday into a savings investment earning a 7 percent compound annual rate of interest. He will continue this savings program for a total of 10 years and then stop making payments. But his savings will continue to compound at 7 percent for 35 more years, until Earl retires at age 65. Ivana Waite also plans to invest $2,000 a year, on each birthday, at 7 percent, and will do so for a total of 35 years. However, she will not begin her contributions until her thirty-first birthday. How much will Earls and Ivanas savings programs be worth at the retirement age of 65? Who is better off financially at retirement, and by how much?
Future value of annuity = A*[(1+r)^n-1]/r FV of single amount = PV*(1+i)^n Value calcualtion for Earl E, Bird: Future value of annuity at age 31 after 10 years = 2000*[(1+.07)^10-1]/.07 = 27633 Value of this annuity fund after 35 years = 27633*(1+.07)^35 = 295025. Ivanas fund value calculation:
ture value of annuity contributions for 35 years = 2000*[(1+.07)^35-1]/.07 = 276473 Comparison: Earl is better off and future value of retirement fund of Earl will be higher by = 295025 276473 = 18551
ANSWER:
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