Question

We are going to make a table tracking the deposits, reserves and loans of a bank as they take in deposits and make loans. Deposits means how much money (which we will call gold) the bank owes to its depositors (people who deposit their money in the bank). Reserves means how much gold the bank has in the vault. Loans means how much gold the bank has loaned (lent?) to people in the form of mortgages, car loans, business loans etc.

Here is the story: There are 100 oz. of gold in the economy. At first, people deposit all 100 in the bank. This increases the bank’s reserves by 100 and also their deposits. I have called this step 1a. But the bank doesn’t need to keep all those reserves, so let’s say that they keep only 10% or 10 oz. as reserves and lend the other 90. I have called this 1b and this represents one full cycle. But then imagine that the 90 oz. of gold that the bank loaned find their way into the pockets of people who sell houses, cars, business stuff, etc. who then deposit them into the bank again. This will increase the bank’s deposits to 190 and their reserves back to 100. I have called this 2a. Now assume that the bank keeps 10% of deposits on reserve and lends the rest out again and fill in 2b. Then assume that the money they loaned out in 2b all gets deposited again and fill in 3a and then 3b. Fill in the table for 7 cycles. Can you see what the Deposits is approaching? Hint: Think about what reserves is approaching. If this takes place an infinite number of times, how many deposits will there be?

Deposits                              Reserves                             Loans

1a           100                                         100

1b           100                                         10                                           90

2a           190                                         100                                         90

2b

3a

3b

4a

4b

5a

5b

6a

6b

7a

7b

Answer 1

		Deposits	Reserves	Loans
1	a	100	100
	b	100	10	90
2	a	190	100	90
	b	190	19	81
3	a	271	100	81
	b	271	27.1	72.9
4	a	343.9	100	72.9
	b	343.9	34.39	65.61
5	a	409.51	100	65.61
	b	409.51	40.951	59.049
6	a	468.559	100	59.049
	b	468.559	46.8559	53.1441
7	a	521.7031	100	53.1441
	b	521.7031	52.17031	47.82969

Using formula for sum of Geometric Progression to find where deposit is approaching,

each periods deposit is 0.9 of the previous period, the first deposit is 100

Therefore, total deposits is sum to infinity in geometric progression series where a = 100 and r = 0.9

Sum to infinity = a/(1-r)

=100/(1-0.9) = 100 /0.1 = 1000