Principles of Macroeconomics / Unit 2 MAC 0136 worked example, 60 to 90 seconds
Computing a Bond's Interest Rate
The idea
For a bond that makes a single payment at maturity, the interest rate is the face value minus the price, divided by the price, times one hundred. Take the face value, which is what the issuer must repay. Subtract the price actually paid, which gives the amount earned for lending. Divide that by the price, because the price is what was lent. Multiply by a hundred to express it as a percentage. The face value stays fixed, so every fall in the price raises the rate, and the relationship is not a straight line: the rate climbs faster as the price falls further.
In practice
Worked example: a bond repays one thousand dollars in a year. Bought for nine hundred and fifty, it earns fifty on nine hundred and fifty, which is about five and three tenths percent. Bought for nine hundred, it earns a hundred on nine hundred, about eleven and one tenth percent. Bought for eight hundred, it earns two hundred on eight hundred, which is twenty-five percent. Halving the price to five hundred gives a rate of one hundred percent.
Where people slip
Divide by the price, not by the face value. Dividing the fifty by one thousand gives five percent rather than five and three tenths, and the error grows as the discount grows, reaching twenty percent instead of twenty-five in the third case.
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