In the example where the reserve ratio is 20%, what is the value of the money…

Concept: In the simple deposit-expansion model of fractional-reserve banking, banks keep back only a fraction r of every deposit as reserves and lend out the rest; the money multiplier is the factor by which total deposits in the banking system can expand from an initial injection of reserves, given by money multiplier = 1 / r, where r is the required reserve ratio expressed as a decimal.

1. Write the formula: money multiplier = 1 / r.

2. Substitute the given reserve ratio: r = 20% = 0.20.

3. Compute the multiplier: 1 / 0.20 = 5.

Cross-check: the same value follows from summing the successive rounds of re-lending as a geometric series — 1 + (1 - r) + (1 - r)² + … = 1 / (1 - (1 - r)) = 1 / r. With r = 0.20 this series also sums to 1 / 0.20 = 5, confirming the result.

The value of the money multiplier is 5.