FINDING THE INTEREST RATE

Thus far we have used Equations 2-1 and 2-2 to find future and present values.
Those equations have four variables, and if we know three of them, we can solve for the fourth. Thus, if we know PV, I, and N, then we can solve 2-1 for FV, while if we know FV, I, and N we can solve 2-2 to find PV. That’s what we did in the preceding two sections.

Now suppose we know PV, FV, and N, and we want to find I. For example, suppose we know that a given bond has a cost of $100 and that it will return $150 after 10 years. Thus, we know PV, FV, and N, and we want to find the rate of return we will earn if we buy the bond. Here’s the situation:

  • FV PV(1 I)N
    $150 $100(1 I)10
    $150/$100 (1 I)10
    1.5 (1 I)10

Unfortunately, we can’t factor I out to produce as simple a formula as we could for FV and PV—we can solve for I, but it requires a bit more algebra.4 However, financial calculators and spreadsheets can find interest rates almost instantly. Here’s the calculator setup: Enter N 10, PV 100, PMT 0 because there are no payments until the security matures, and FV 150. Then, when you press the I/YR key, the calcula- tor gives the answer, 4.14 percent. You would get this same answer with a spreadsheet.

  • The U.S. Treasury offers to sell you a bond for $585.43. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond for $585.43? What rate would you earn if you could buy the bond for $550? For $600? (5.5%; 6.16%; 5.24%)
  • Microsoft earned $0.12 per share in 1994. Ten years later, in 2004, it earned $1.04. What was the growth rate in Microsoft’s earnings per share (EPS) over the 10-year period? If EPS in 2004 had been $0.65 rather than $1.04, what would the growth rate have been? (24.1%; 18.41%)