# 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.

## 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.