Chapter 25, Problem 16P

To determine

(a)

To compute:

The amount of money the bank could lend if a bank had a reserve of $30,000 and demand deposits of $200,000.

Answer to Problem 16P

The amount of money that could be lent if the bank faces the given required reserve is as shown below:

$10\text{percent}$	$\$180,000$
$\text{15 percent}$	$\$170,000$
$20\text{percent}$	$\$160,000$

Explanation of Solution

Given information:

The bank had reservesof $\$30,000$ and demand deposits of $200,000. The bank reserve ratio is 10%.

Calculation of required reserve:

  $\begin{array}{c}\text{Required}\text{reserve}=r\times \text{D}\\ =0.1\times \$200,000\\ =\$20,000\end{array}$

Calculation of excess reserve:

  $\begin{array}{c}\text{Excess}\text{reserve}=\text{Actual}\text{reserve}-\text{Required}\text{reserve}\\ =\$\text{30,000}-\$\text{20,000}\\ =\$10,000\end{array}$

The assets and liability of the bank should be equal.

Therefore,

  $\begin{array}{c}\text{Demand}\text{depoists}+\text{Excess}\text{reserve}=\text{Reserve}+\text{Loans}\\ \$200,000+\$10,000=\$30,000+\text{Loans}\\ \text{Loans}=\$210,000-\$30,000\\ =\$180,000\end{array}$

Similarly,

The bank had reservesof $\$30,000$ and demand deposits of $200,000. The bank reserve ratio is 15%.

Calculation of required reserve:

  $\begin{array}{c}\text{Required}\text{reserve}=r\times \text{D}\\ =0.15\times \$200,000\\ =\$30,000\end{array}$

Calculation of excess reserve:

  $\begin{array}{c}\text{Excess}\text{reserve}=\text{Actual}\text{reserve}-\text{Required}\text{reserve}\\ =\$\text{30,000}-\$3\text{0,000}\\ =\$0\end{array}$

The assets and liability of the bank should be equal. Therefore,

  $\begin{array}{c}\text{Demand}\text{depoists}+\text{Excess}\text{reserve}=\text{Reserve}+\text{Loans}\\ \$200,000+0=\$30,000+\text{Loans}\\ \text{Loans}=\$200,000-\$30,000\\ =\$170,000\end{array}$

And

The bank had reservesof $\$30,000$ and demand deposits of $200,000. The bank reserve ratio is 20%.

Calculation of required reserve:

  $\begin{array}{c}\text{Required}\text{reserve}=r\times \text{D}\\ =0.2\times \$200,000\\ =\$40,000\end{array}$

Calculation of excess reserve:

  $\begin{array}{c}\text{Excess}\text{reserve}=\text{Actual}\text{reserve}-\text{Required}\text{reserve}\\ =\$\text{30,000}-\$4\text{0,000}\\ =-\$10,000\end{array}$

The assets and liability of the bank should be equal. Therefore,

  $\begin{array}{c}\text{Demand}\text{depoists}+\text{Excess}\text{reserve}=\text{Reserve}+\text{Loans}\\ \$200,000+\left(-\$10,000\right)=\$30,000+\text{Loans}\\ \text{Loans}=\$190,000-\$30,000\\ =\$160,000\end{array}$

Economics Concept Introduction

Required reserve:

It refers to a certain amount of cash from the deposits that banks need to keep according to the guidelines of central bank.

Required reserve is calculated by,

  $RR=r\times D$

Here, RR is required reserve, r is percentage of required reserve and D is the total amount in

deposits.

Excess reserve:

The holding of reserves in excess by the banks or financial institutions than what is required by the regulators, creditors or internal controls is termed as excess reserve or capital reserve.

  $\text{ER}=\text{Cash}\text{Reserve}-\text{Required}\text{Reserve}$

Money multiplier:

It calculates the potential amount of money a bank generates with each dollar of reserves.

  $\text{Money}\text{multiplier}=\frac{1}{\text{R}}$

Where, R is required reserve.

To determine

(b)

To compute:

The additional dollar that can be lent out as a result of $40,000 deposit.

Answer to Problem 16P

The additional dollar that can be lent out as a result of $40,000 deposit if the bank faces the given required reserve ratio is shown in the table below:

$10\text{percent}$	$\$176,000$
$15\text{percent}$	$\$110,000$
$20\text{percent}$	$\$152,000$

Explanation of Solution

Given information:

The bank has reserve of $30,000 with new demand deposit of $240,000.

The bank must keep demand deposit with Fed of 10%.

The reserves with bank are $30,000 and demand deposits are $240,000. The bank reserve ratio is 10%.

Calculation of required reserve:

  $\begin{array}{c}\text{Required}\text{reserve}=r\times \text{D}\\ =0.1\times \$240,000\\ =\$24,000\end{array}$

Calculation of excess reserve:

  $\begin{array}{c}\text{Excess}\text{reserve}=\text{Actual}\text{reserve}-\text{Required}\text{reserve}\\ =\$\text{30,000}-\$\text{24,000}\\ =\$6,000\end{array}$

The assets and liability of the bank should be equal. Therefore,

  $\begin{array}{c}\text{Demand}\text{depoists}+\text{Excess}\text{reserve}=\text{Reserve}+\text{Loans}\\ \$200,000+\$6,000=\$30,000+\text{Loans}\\ \text{Loans}=\$206,000-\$30,000\\ =\$176,000\end{array}$

Therefore, bank can lend an amount of $\$176,000$ with reserve ratio of $10\%.$

Similarly,

The reserves with bank are $30,000 and demand deposits are $240,000. The bank reserve ratio is 15%.

Calculation of required reserve:

  $\begin{array}{c}\text{Required}\text{reserve}=r\times \text{D}\\ =0.15\times \$240,000\\ =\$36,000\end{array}$

Calculation of excess reserve:-

  $\begin{array}{c}\text{Excess}\text{reserve}=\text{Actual}\text{reserve}-\text{Required}\text{reserve}\\ =\$\text{30,000}-\$36\text{,000}\\ =-\$6,000\end{array}$

The assets and liability of the bank should be equal. Therefore,

  $\begin{array}{c}\text{Demand}\text{depoists}+\text{Excess}\text{reserve}=\text{Reserve}+\text{Loans}\\ \$240,000+\left(-\$6,000\right)=\$30,000+\text{Loans}\\ \text{Loans}=\$110,000\end{array}$

Therefore, bank can lend an amount of $\$110,000$ with reserve ratio $15\%.$

And,

The reserves with bank are $30,000 and demand deposits are $240,000. The bank reserve ratio is 15%.

Calculation of required reserve:

  $\begin{array}{c}\text{Required}\text{reserve}=r\times \text{D}\\ =0.2\times \$240,000\\ =\$48,000\end{array}$

Calculation of excess reserve:-

  $\begin{array}{c}\text{Excess}\text{reserve}=\text{Actual}\text{reserve}-\text{Required}\text{reserve}\\ =\$\text{30,000}-\$48\text{,000}\\ =-\$18,000\end{array}$

The assets and liability of the bank should be equal. Therefore,

  $\begin{array}{c}\text{Demand}\text{depoists}+\text{Excess}\text{reserve}=\text{Reserve}+\text{Loans}\\ \$240,000+\left(-\$48,000\right)=\$30,000+\text{Loans}\\ \text{Loans}=\$182,000-\$30,000\\ =\$152,000\end{array}$

Therefore, bank can lend an amount of $\$152,000$ with reserve ratio $20\%.$

Economics Concept Introduction

Required reserve:

It refers to a certain amount of cash from the deposits that banks need to keep according to the guidelines of central bank.

Required reserve is calculated by,

  $RR=r\times D$

Here, RR is required reserve, r is percentage of required reserve and D is the total amount in

deposits.

Excess reserve:

The holding of reserves in excess by the banks or financial institutions than what is required by the regulators, creditors or internal controls is termed as excess reserve or capital reserve.

  $\text{ER}=\text{Cash}\text{Reserve}-\text{Required}\text{Reserve}$

Money multiplier:

It calculates the potential amount of money a bank generates with each dollar of reserves.

  $\text{Money}\text{multiplier}=\frac{1}{\text{R}}$

Where, R is required reserve.