Question

A bank received an initial deposit of $9,000, kept a percentage of this money in reserve based on a reserve rate of 9% and loaned out the rest. The amount it loaned out all was eventually deposited back into the bank. if this cycle continued indefinitely, how much money eventually resulted from the initial deposit?

Answer 1

Answer: $100,000

Explanation:

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Answer 2

The initial deposit is $9,000. The bank kept 9% of this amount in reserve and landed out the rest. So, the bank kept $810 as reserve and loaned out as $8190. The process repeated itself and this time the bank kept $737.10 as reserve and loaned out as $7452.90. This process will repeat itself indefinitely.

So, we will have a geometric series with r< 1 and with infinite terms.

Also, the total money creation is initial deposit times money multiplier.

Here Money multiplier =
`(1)/(reserve rate) = (1)/(0.09)`

Hence, the money creation =
`9000 * (1)/(0.09) = 100,000`

So, the total money that resulted from the initial investment is $100,000.