Interest Rate

An interest rate is a contract term. When a bank lends 10,000 at 6% a year, both sides know before the money changes hands that the borrower owes 600 of interest for each year the loan is outstanding. That certainty about the promised payment separates an interest rate from a rate of return, which can only be measured once the outcome is known, and from a yield, which is backed out of a market price that changes daily.

Interest compensates for two things: giving up the use of money for a period, and accepting the risk that it will not come back in full. The first part is common to every borrower in a currency; the second depends on who is borrowing, for how long and on what terms.

Analysts decompose an interest rate into layers. The base is the real risk-free rate, the reward for postponing consumption when there is neither default risk nor inflation. Adding compensation for expected inflation gives the nominal risk-free rate, which yields on short-term government bills approximate in practice. On top come premiums tied to the borrower and the instrument: a default risk premium for the chance of not being repaid, a liquidity premium for debt that is hard to sell quickly at a fair price, and a maturity premium for the greater price sensitivity of longer-term debt.

The sum is an approximation. The real rate and inflation combine multiplicatively, so exactly 1 + r_NF = (1 + r_RF) × (1 + inf), where r_NF is the nominal risk-free rate, r_RF the real risk-free rate and inf expected inflation.

The same rate can play three roles, depending on the question being asked. For a saver or lender it is a required rate of return: the minimum compensation needed to part with money for the period. In a valuation it is a discount rate: the rate that converts a future cash flow into its value today, so that 1,060 receivable in a year is worth 1,000 now at 6%. In a choice between spending and saving it is an opportunity cost: the return given up by consuming now.

These are not three different rates but three uses of one. In a time value of money problem, identify which role the rate plays, because it determines whether cash flows are being compounded forward or discounted back.

Market interest rates move with central bank policy, inflation expectations and the demand for credit. When they rise, the fixed payments promised by existing bonds become less attractive, so bond prices fall; when they drop, prices rise. The size of the move depends on the bond's duration.

On the exam, interest rates appear in time value of money calculations, in conversions between quoted and effective rates, and in building required returns from components. Watch the quoting convention: a stated annual rate compounded monthly is not an effective annual rate. The exact effective rate is (1 + r_s / m)^m − 1, where r_s is the stated annual rate and m is how many times a year interest compounds.