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Homework answers / question archive / An insurance agent offers services to clients who are concerned about their personal financial planning for retirement
An insurance agent offers services to clients who are concerned about their personal financial planning for retirement. To emphasize the advantages of an early start to? investing, she points out that a? 25-year-old person who saves ?$1500a year for 10 years? (and makes no more contributions after age? 34) will earn more than by waiting 10 years and then saving ?$1500a year from age 35 until retirement at age 65? (a total of 30? contributions). Find the net earnings? (compound amount minus total? contributions) at age 65 for both situations. Assume an effective annual rate of 7?%, and suppose that deposits are made at the beginning of each year.
The net earnings at age 65 when investing for 10 years starting at age 25 are ???? ?$
and, the net earnings at age 65 when investing for 30 years starting at age 35 are ?
The net earnings at age 65 when investing for 10 years starting at age 25:
Two steps:
Step 1: Future value of annuity due with n = 10, r=7% and P = 1500
P* (((1+r)^n)-1)*(1+r)/r = 1500*(((1+7%)^10)-1)*(1+7%)/7% = 22175.40
Step 2: Compounded value of this sum 30 years later at 7% = 22175.40*(1+7%)^30 = 168804.80
Net earnings = 168804.80 - 1500*10 = 153804.80
The net earnings at age 65 when investing for 30 years starting at age 35
Future value of annuity due with n = 30, r=7% and P = 1500
P* (((1+r)^n)-1)*(1+r)/r = 1500*(((1+7%)^30)-1)*(1+7%)/7% = 151609.56
Net earnings = 151609.56 - 1500*30 = 106609.56
