Problem

Present and future values of a cash flow stream

An investment will pay $50 at the end of each of the next 3 years, $250 at the end of Year 4, $400 at the end of Year 5, and $550 at the end of Year 6.

If other investments of equal risk earn 7% annually, what is its present value? Round your answer to the nearest cent.

$  

If other investments of equal risk earn 7% annually, what is its future value? Round your answer to the nearest cent.

$  

Problem

Present value of an annuity

Find the present values of these ordinary annuities. Discounting occurs once a year. Round your answers to the nearest cent.

$900 per year for 12 years at 14%.

$  

$450 per year for 6 years at 7%.

$  

$600 per year for 12 years at 0%.

$  

Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent.

$900 per year for 12 years at 14%.

$  

$450 per year for 6 years at 7%.

$  

$600 per year for 12 years at 0%.

$  

Problem

Future value of an annuity

Your client is 25 years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $10,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 9% in the future.

If she follows your advice, how much money will she have at 65? Round your answer to the nearest cent.

$  

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

$  

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: $

Annual withdrawals if she retires at 70: $