What an interest rate is made of

One rate, three readings

Money today is worth more than the same amount later, because it can be spent or invested now. An interest rate (or yield) is the rate of return that makes a sum today and a sum later equal in value.

Suppose you are indifferent between NOK 47,000 today and NOK 50,000 in a year. The extra NOK 3,000 is your compensation for waiting, and 3,000 / 47,000 ≈ 6.38% is the interest rate.

That single 6.38% can be described in three ways, depending on whose decision you look at. None is more correct than the others; they are three angles on one number.

Exam stems give the reading away through wording: 'minimum return to accept' → required return; 'value today of' → discount rate; 'instead of spending' or 'forgone' → opportunity cost. 'Interest rate' and 'discount rate' are used almost interchangeably.

Building a rate from its parts

Market interest rates are set by the supply of funds (from savers) and the demand for funds (from borrowers). From the lender's side, any rate can be split into a base rate for pure waiting plus a premium for each separate risk the lender takes on.

The real risk-free rate is the one-period rate on a completely safe security when no inflation is expected. It reflects time preference: how much extra future consumption people need before they give up consumption today.

The inflation premium covers the expected loss of purchasing power, averaged over the life of the debt. The default risk premium covers the chance that the borrower pays late or pays less than promised.

The liquidity premium covers the loss versus fair value if you must turn the investment into cash quickly. Large government bill issues trade easily and carry none; bonds of small issuers trade rarely and carry one. The maturity premium covers the fact that the price of longer-dated debt moves more when market rates change.

Every component changes over time, so every market rate moves. How much a particular rate moves depends on which premiums it carries and on what investors expect the economy to do.

Nominal versus real, and the risk-free benchmark

Combining the real risk-free rate and the inflation premium gives the nominal risk-free rate. The exact link is multiplicative, $(1+r_{\text{nom}}) = (1+r_{\text{real}})(1+\pi)$, because inflation also erodes the real return itself. In practice the simple sum is used as an approximation.

With a real rate of 1.2% and expected inflation of 2.3%, the sum gives 3.5% and the exact form gives 1.012 × 1.023 − 1 = 3.53%. The gap is small at low rates; use the exact form when answer options sit close together.

Short-term government bills, such as a 3-month bill, serve as the nominal risk-free rate for their country and horizon. They carry essentially no default, liquidity or maturity premium: only the real rate and expected inflation.

Rates are quoted on an annual basis. A 90-day bill quoted at 3% does not pay 3% over its 90 days; it pays roughly 3% × 90/365 ≈ 0.74%.

Isolating one premium at a time

Exam questions often give a table of bonds and ask you to back out a premium. Find two securities that differ in exactly one feature: their yield gap is the premium for that feature.

If no clean pair exists, peel off a premium you already know first. If two bonds differ in both liquidity and default risk, and you already know the liquidity premium, the rest of the gap is the default premium.

For an unknown yield, set bounds. A bond that is longer than an otherwise identical bond must yield more (larger maturity premium). A bond that is shorter than another must yield less, once you adjust for any premium the two do not share.