I Consider a future value of $1,050,000 whose present value is $1,000,000.

1. If its futurity is 1 year, what is the implied interest, or discount, rate?
2. What if its futurity is 2 years?
3. What if its futurity is 1 year but its present value is 990,000?
4. What if its futurity is 2 years, its present value is 1,000,000 but semi-annually compounded?

II Today is September 10. Consider a cash flow of $1,000,000 to be paid in six months whose price is $990,000. What is its implied interest rate?

III Consider a five-year annuity which pays $10,000. If its price is $46,458 what must be the implied discount rate, or yield?

What if it is a perpetuity?

IV Consider a five-year bond with a face value of 100 and 4% coupon rate. If its price is par what is the implied yield to maturity?

What if its price is 100.2229?

V You are considering investing in a business whose cash flows are expected to be $990,000 next year, $1,000,000 in the following year and $2,600,000 in the third. If your required investment is $3,600,000 what is the internal rate-of-return (IROR)? [In other words, what is the discount rate that, when applied to these future cash flows, equates the present value to the investment amount?]