The relation between inflation rate (a), real interest rate (b) and market interest rate (c) can be

Question

The relation between inflation rate (a), real interest rate (b) and market interest rate (c) can be best given as

Examoogle · Accepted Answer

$c = a + b + ab$

Explanation: The relationship between market interest rate, real interest rate, and inflation is defined by the Fisher Equation. When compounded, the market rate $c$ accounts for the erosion of purchasing power due to inflation $a$ by adding the product of inflation and the real rate $b$.

Working Principle: The relationship is derived from the growth of an investment over one period. If $P$ is the principal, the future value at market rate $c$ is $P(1+c)$. The purchasing power is adjusted by inflation $a$, such that the real growth is $P(1+b)$. Equating these gives $1+c = (1+a)(1+b)$, which expands to $1+c = 1 + a + b + ab$, simplifying to $c = a + b + ab$.

Key Formulas: $1 + c = (1 + a)(1 + b)$ — Basic derivation of the Fisher effect; $c = a + b + ab$ — Final relation for the market interest rate

Key Points: The term $ab$ represents the cross-product effect, which becomes significant during periods of high inflation.; For low inflation rates, the approximation $c \approx a + b$ is commonly used in simplified engineering economics.; $c$ is the nominal (market) rate, $a$ is the inflation rate, and $b$ is the real interest rate.; All rates $a, b, c$ must be expressed as decimals in the calculation.

Advantages: Provides an accurate mathematical model for capital investment analysis under inflation.; Ensures that the real returns on investment are correctly calculated by accounting for price changes.

Disadvantages: The exact formula is often ignored in favor of the approximation $c = a + b$ when rates are very small.; Assumes constant inflation over the investment period, which is rarely true in volatile economies.

Applications: Corporate finance and capital budgeting.; Evaluating long-term project viability under inflationary economic conditions.

Additional Info: The approximation $c \approx a + b$ is known as the 'Fisher Approximation'.. Option C ($c = a + b$) is only an approximation valid when both $a$ and $b$ are very small, making the product $ab$ negligible.

Answer: A is correct — The market interest rate is exactly related to the inflation and real interest rates by the compound growth formula $c = a + b + ab$.

Exam Tip: In competitive exams, always check if the question implies exact calculation (use $ab$ term) or simplified estimation ($c = a + b$); if both are present, the exact formula is the technically superior choice.

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