Future value

Problem 5-14  
Future value of an annuity  
Find the future values of these ordinary annuities. Compounding occurs once a year. Round your answers to the nearest cent.  
a. $1,000 per year for 12 years at 16%.  
b. $500 per year for 6 years at 8%.  
c. $500 per year for 16 years at 0%.  
Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent.  
d. $1,000 per year for 12 years at 16%.  
e. $500 per year for 6 years at 8%.  
f. $500 per year for 16 years at 0%.  
Problem 5-19
Future value of an annuity
Your client is 21 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $6,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 12% in the future.
a. If she follows your advice, how much money will she have at 65? Round your answer to the nearest cent.
 

b. How much will she have at 70? Round your answer to the nearest cent.

c. She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age? Round your answers to the nearest cent.

Annual withdrawals if she retires at 65

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