Today is t=0. Consider the following two financial instruments. Instrument A never pays interest income but does pay $2,000 in year t=4. Instrument B pays $40 interest income in years t=1, t=2, and t=3. In addition, in year t=4, instrument B will also pay $2,000.

a. Find the price of each instrument at t=0 when the appropriate interest rate is 4%. Note that the price of an instrument is the present value of the cash flows that the instrument generates.

b. Find the price of each instrument at t=0 when the interest rate is 3%.

c. Suppose you purchased both instruments when the market interest rate was 4%. Within a very short period, the market interest rate suddenly falls to 1%. Which instrument will show the largest I) dollar change in price? ii) percentage change in price? How would you explain your result?

The main thing to know is exactly what's stated in part (a): The price of a security is the PV of its cash flows. Step by step, (1) determine exactly what the instrument's cash flows are, and when they occur; (2) calculate the present value of each cash flow; and (3) add up the individual cash flow PVs. That sum is the instrument's price.

Any cash flow, where its amount is C, it occurs at time t, and where the discount rate is r, will have a present value of

\frac{C}{(1+r)^t}

In your given problem, note that Security A has a single cash flow, whereas Instrument B has 40, 40, 40, and 2,040. (It's OK to add two cash flows together, and treat them as a single amount, when they occur simultaneously.)

For parts (a), (b), and (c), r is 0.04, 0.03, and 0.01, respectively.

I'll leave you with a hint re your last question: The PV of cash flows occurring further in the future are more sensitive to interest rate movements; "nearer" cash flows are relatively less sensitive.