Q.A customer deposits ₹20,000 of cash with a bank. If every bank in the system keeps a cash reserve ratio of 25%, how much total deposits (credit) can the banking system create, and how much of it is derivative deposit?

The total deposits the system can create equal the primary deposit multiplied by the credit multiplier (1 ÷ reserve ratio).

Given: primary deposit = ₹20,000; cash reserve ratio r = 25% = 0.25.

Step 1 — credit multiplier. The credit multiplier is 1 ÷ r = 1 ÷ 0.25 = 4.

Step 2 — total deposits created. Total deposits = primary deposit × multiplier = ₹20,000 × 4 = ₹80,000.

Step 3 — derivative deposit. Derivative (created) deposit = total deposits − primary deposit = ₹80,000 − ₹20,000 = ₹60,000.

Verification (independent check). Adding the chain of loans directly: the first bank keeps 25% of ₹20,000 = ₹5,000 and lends ₹15,000; the next keeps ₹3,750 and lends ₹11,250; the next lends ₹8,437.50; and so on. This is a geometric series with first term ₹15,000 and common ratio 0.75, whose sum is ₹15,000 ÷ (1 − 0.75) = ₹15,000 ÷ 0.25 = ₹60,000 of derivative deposits — which, added to the ₹20,000 primary deposit, again gives ₹80,000 total. The two methods agree.

Alternative (series) method: sum the successive loans as a geometric progression — first loan = deposit × (1 − r) = ₹15,000, common ratio = (1 − r) = 0.75, sum = ₹15,000 ÷ (1 − 0.75) = ₹60,000 derivative deposit; add the ₹20,000 primary deposit to get ₹80,000 total. This gives the same result as the multiplier formula.

A frequent mistake is to report ₹80,000 as the 'credit created' — but the created (derivative) credit is ₹60,000; the ₹80,000 is total deposits including the original ₹20,000. Another slip is using r as 25 instead of 0.25 in the formula.