Question

What are the steps a $500 deposit takes, to become $4,500 in loans, in a fractional reserve system with a 10% reserve ratio?

Answer 1

you can solve the equation
500 + 500*.90 + 500 *.90^2 + ... = 4500

Answer 2

where does the .90 come from?

Answer 3

Can you explain what the numbers stand for so I can understand for future?

Answer 4

the bank has to keep 10% in reserves, so it can loan out 90%

Answer 5

so a person deposits 500 dollars.
the bank turns around and lends out 90% of the 500 dollars (because it has to keep 10% in reserves) .
so the bank lends out 500*.90 = 450 dollars.

Answer 6

then how do I end up with $4,500?

Answer 7

so I keep doing this until it eventually adds up to $4500

Answer 8

The bank gets a deposit of 500.
The bank keeps in reserves 10% of the 500 dollars (50 dollars) in reserves, just in case the original depositer comes back to ask for his money back.
Now the bank is free to lend 450 dollars in loan, and we assume that the bank always does lend out the money.
Now the person whom the bank loaned out the 450 dollars, lets say he uses to pay his workers or services and these people eventually bring back the 450 dollars to deposit in the bank.
Now the bank can loan out 90% of that 450 dollars (keeps 10% in reserves)
so the bank can loan out 405 dollars.

and this process continues

Answer 9

Ok, but will the loans eventually add up to $4,500?

Answer 10

yes.
500*.9 + 500 * .9 ^2 + 500 *.9^2 +...
=$450 loan + $405 loan + $364.5 loan+

Answer 11

Thank you!! You are the bomb!!

Answer 12

we can find how many steps it takes using a geometric series

Answer 13

$$
\Large {
\sum_{k=1}^{n}500 \cdot (0.9)^k = 4500



}$$

Answer 14

The amount you can loan out shrinks and you can never exactly reach being able to loan out 4500 , but you can loan out 4499 after say a hundred times of doing this