Question

A bank received an initial deposit of $12,00, kept a percentage of this money in reserve based on a reserve rate of 6%, and the loaned out the rest. The amount it loaned out eventually was all deposited back into the bank. If this cycle continued indefinitely, how much money eventually resulted from the initial deposit

Answer 1

Answer:

If this cycle continued indefinitely, how much money that eventually resulted from the initial deposit is

500,000 (C is the answer)

Answer 2

$200,000

Explanation:

The total amount deposited is the sum of an infinite geometric series. The first term of the series is $12,000, and the common ratio is 1 -0.06 = 0.94.

That is, 0.94 times $12,000 is loaned after the first deposit. When that loan amount is all deposited, 6% is kept in reserve, and $12,000×0.94² is loaned after that deposit.

Sum formula

The formula for the sum of an infinite geometric series is ...

S = a/(1 -r)

where 'a' is the first term, and r is the common ratio..

Application

For the given series, a=12000, and r=0.94 so the sum is ...

S = 12000/(1 -0.94) = 12000/0.06 = 200,000

The result of the initial deposit will eventually be $200,000.

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Additional comment

In economics, the inverse of the reserve ratio is called the "deposit multiplier."