What is the effective annual rate (EAR) if the stated rate is 8 percent and compounding occur semiannually? Quarterly?
PROBLEM 1

Find the following values for a lump sum:

– The future value of $500 invested at 8 percent for one year

– The future value of $500 invested at 8 percent for five years

– The present value of $500 to be received in one year when the opportunity cost rate is 8 percent

– The present value of $500 to be received in five years when the opportunity cost rate is 8 percent

assuming:

Annual compounding
Semiannual compounding
Quarterly compounding
PROBLEM 2

What is the effective annual rate (EAR) if the stated rate is 8 percent and compounding occur semiannually? Quarterly?

ANSWER

PROBLEM 3

Find the following values assuming a regular, or ordinary, annuity:

– The present value of $400 per year for ten years at 10 percent

– The future value of $400 per year for ten years at 10 percent

– The present value of $200 per year for five years at 5 percent

– The future value of $200 per year for five years at 5 percent

assuming:

A regular or ordinary annuity
An annuity due
ANSWER

PROBLEM 4

Consider the following uneven cash flow stream:

Year Cash Flow

0 $0

1 $250

2 $400

3 $500

4 $600

5 $600

What is the present (Year 0) value if the opportunity cost (discount) rate is 10 percent?
Add an outflow (or cost) of $1,000 at Year 0. What is the present value (or net present value) of the
stream?

ANSWER

PROBLEM 5

Consider another uneven cash flow stream:

Year Cash Flow

0 $2,000

1 $2,000

2 $0

3 $1,500

4 $2,500

5 $4,000

What is the present (Year 0) value of the cash flow stream if the opportunity cost rate is 10 percent?
What is the value of the cash flow stream at the end of Year 5 if the cash flows are invested in an
account that pays 10 percent annually?

What cash flow today (Year 0), in lieu of the $2,000 cash flow, would be needed to accumulate $20,000
at the end of Year 5? (Assume that the cash flows for Years 1 through 5 remain the same.)

Time value analysis involves either discounting or compounding cash flows. Many healthcare financial

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