The Norfolk Bank has $18,000 in excess reservces and the reserve ratio is 20 percent. Which level of checkable deposits and reserves might this bank hold?
a. $160,000 in checkable-deposit liabilities and $47,000 in reserves.
b. $140,00 in checkable-deposit liabilities and $46,000 in reserves
c. $120,000 in cehckable-deposit liabilities and $32,000 in reserves
d. $100,000 in checkable-deposit liabilites and $30,000 in reserves
Use algebra. Total reserves are required reserves plus excess reserves.
Required reserves are .2*liabilities, and your are given excess reserves. So, simply multiply the reserve requirement ratio to each of the liability amounts to find the correct answer.
b. $140,00 in checkable-deposit liabilities and $46,000 in reserves
Let's solve this step by step:
Step 1: Calculate the required reserves using the reserve ratio.
Required reserves = Reserve ratio * Checkable-deposit liabilities
Step 2: Calculate the total reserves by adding the excess reserves to the required reserves.
Total reserves = Required reserves + Excess reserves
Now let's calculate the total reserves for each option:
a. Total reserves = (0.2 * $160,000) + $18,000
= $32,000 + $18,000
= $50,000
b. Total reserves = (0.2 * $140,000) + $18,000
= $28,000 + $18,000
= $46,000
c. Total reserves = (0.2 * $120,000) + $18,000
= $24,000 + $18,000
= $42,000
d. Total reserves = (0.2 * $100,000) + $18,000
= $20,000 + $18,000
= $38,000
Among the given options, the correct answer is:
c. $120,000 in checkable-deposit liabilities and $32,000 in reserves
To solve this problem using algebra, we need to use the given reserve ratio and excess reserves. Let's go through each option to see which one satisfies the given conditions.
Option a: $160,000 in checkable-deposit liabilities and $47,000 in reserves.
Using the formula for required reserves, we can calculate the required reserves for this option:
Required reserves = 0.20 * $160,000 = $32,000
Since the excess reserves are given as $18,000, the total reserves would be:
Total reserves = Required reserves + Excess reserves = $32,000 + $18,000 = $50,000
However, this does not match the $47,000 in reserves given.
Option b: $140,000 in checkable-deposit liabilities and $46,000 in reserves.
Using the same calculations:
Required reserves = 0.20 * $140,000 = $28,000
Total reserves = $28,000 + $18,000 = $46,000
This matches the $46,000 in reserves given, so let's check the liabilities next.
Option c: $120,000 in checkable-deposit liabilities and $32,000 in reserves.
Required reserves = 0.20 * $120,000 = $24,000
Total reserves = $24,000 + $18,000 = $42,000
This does not match the $32,000 in reserves given.
Option d: $100,000 in checkable-deposit liabilities and $30,000 in reserves.
Required reserves = 0.20 * $100,000 = $20,000
Total reserves = $20,000 + $18,000 = $38,000
This does not match the $30,000 in reserves given.
Therefore, the correct answer is option b: $140,000 in checkable-deposit liabilities and $46,000 in reserves.