Chapter 17, Problem 13P

To determine

(a)

To compute:

The excess reserve created by the deposit of $100,000 for the given reserve requirements.

Answer to Problem 13P

The required reserve created by$100,000 if the bank faces the given reserve requirement is as shown below:

$10\text{percent}$	$\$10,000$
$20\text{percent}$	$\$20,000$
$25\text{percent}$	$\$25,000$
$50\text{percent}$	$\$50,000$

Explanation of Solution

The required reserve created by $100,000 if the bank faces the requirement of reserve ratio of 10%:

  $\begin{array}{c}\text{Required}\text{Reserve}=\mathrm{Reserve}ratio\times \text{Deposits}\\ =0.1\times 100,000\\ =\$10,000\end{array}$

The required reserve created by$100,000if the bank faces the requirement of reserve ratio of 20%:

  $\begin{array}{c}\text{Required}\text{Reserve}=\mathrm{Reserve}ratio\times \text{Deposits}\\ =0.2\times \$100,000\\ =\$20,000\end{array}$

The required reserve created by$100,000 if the bank faces the requirement of reserve ratio of 25%:

  $\begin{array}{c}\text{Required}\text{Reserve}=\mathrm{Reserve}ratio\times \text{Deposits}\\ =0.25\times \$100,000\\ =\$25,000\end{array}$

The required reserve created by$100,000 if the bank faces the requirement of reserve ratio of 50%:

  $\begin{array}{c}\text{Required}\text{Reserve}=\mathrm{Reserve}ratio\times \text{Deposits}\\ =0.5\times \$100,000\\ =\$50,000\end{array}$

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 $100,000 deposit for the given reserve requirements.

Answer to Problem 13P

The additional dollar that can be lent out as a result of $100,000 deposit if the bank faces the given reserve requirements is as shown below:

$10\text{percent}$	$\$90,000$
$20\text{percent}$	$\$80,000$
$25\text{percent}$	$\$75,000$
$50\text{percent}$	$\$50,000$

Explanation of Solution

If the initial deposit is $\$100,000$ with required reserve as $\$10,000$.

Calculation for excess reserve:

  $\begin{array}{c}\text{ER}=\text{Cash}\text{Reserve}-\text{Required}\text{Reserve}\\ \text{= \$100,000}-\$10,000\\ =\$90,000\end{array}$

If the initial deposit is $\$100,000$ with required reserve as $\$20,000$.

Calculation for excess reserve:

  $\begin{array}{c}\text{ER}=\text{Cash}\text{Reserve}-\text{Required}\text{Reserve}\\ =\$\text{100,000}-\$20,000\\ =\$80,000\end{array}$

If the initial deposit is $\$100,000$ with required reserve as $\$25,000$

Calculation for excess reserve:

  $\begin{array}{c}\text{ER}=\text{Cash}\text{Reserve}-\text{Required}\text{Reserve}\\ =\$\text{100,000}-\$25,000\\ =\$75,000\end{array}$

If the initial deposit is $\$100,000$ with required reserve as $\$50,000$

Calculation for excess reserve:

  $\begin{array}{c}\text{ER}=\text{Cash}\text{Reserve}-\text{Required}\text{Reserve}\\ =\text{\$100,000}-\$50,000\\ =\$50,000\end{array}$

Working note:

The required reserve created by $\$100,000$ if the bank faces the reserve ratio is $10\%$ :

  $\begin{array}{c}\text{Required}\text{Reserve}=\mathrm{Reserve}ratio\times \text{Deposits}\\ =0.1\times \$100,000\\ =\$10,000\end{array}$

The required reserve created by $\$100,000$ if the bank faces the reserve ratio is $20\%$ :

  $\begin{array}{c}\text{Required}\text{Reserve}=\mathrm{Reserve}ratio\times \text{Deposits}\\ =0.2\times \$100,000\\ =\$20,000\end{array}$

The required reserve created by $\$100,000$ if the bank faces the reserve ratio is $25\%$ :

  $\begin{array}{c}\text{Required}\text{Reserve}=\mathrm{Reserve}ratio\times \text{Deposits}\\ =0.25\times \$100,000\\ =\$25,000\end{array}$

The required reserve created by $\$100,000$ if the bank faces the reserve ratio is $50\%$ :

  $\begin{array}{c}\text{Required}\text{Reserve}=\mathrm{Reserve}ratio\times \text{Deposits}\\ =0.5\times \$100,000\\ =\$50,000\end{array}$

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

(c)

To compute:

The additional dollar that can be created by bank in response of a $100,000 deposit for the given reserve requirements.

Answer to Problem 13P

The additional dollar that can be created as a result of $\$100,000$ deposit if the bank faces the given reserve requirementsis as shown below:

$10\text{percent}$	$\text{\$ 1,000,000}$
$20\text{percent}$	$\text{\$ 500,000}$
$25\text{percent}$	$\text{\$ 400,000}$
$50\text{percent}$	$\text{\$ 200,000}$

Explanation of Solution

Potential money can be calculated for reserve ratio of $10\%.$

  $\begin{array}{c}\text{Potential}\text{Money}=\text{Initial}\text{Deposit}\times \text{Money}\text{Multiplier}\\ =\text{\$100,000}\times \text{10}\\ =\text{\$1,000,000}\end{array}$

Potential money can be calculated for reserve ratio of $20\%.$

  $\begin{array}{c}\text{Potential}\text{Money}=\text{Initial}\text{Deposit}\times \text{Money}\text{Multiplier}\\ =\text{\$100,000}\times 5\\ =\text{\$500,000}\end{array}$

Potential money can be calculated for reserve ratio of $25\%.$

  $\begin{array}{c}\text{Potential}\text{Money}=\text{Initial}\text{Deposit}\times \text{Money}\text{Multiplier}\\ =\text{\$100,000}\times 4\\ =\text{\$400,000}\end{array}$

Potential money can be calculated for reserve ratio of $50\%.$

  $\begin{array}{c}\text{Potential}\text{Money}=\text{Initial}\text{Deposit}\times \text{Money}\text{Multiplier}\\ =\text{\$100,000}\times 2\\ =\text{\$200,000}\end{array}$

Working note:

Calculation of money multiplier for reserve ratio of 10%:

  $\begin{array}{c}\text{Money multiplier}=\frac{1}{R}\\ =\frac{1}{0.1}\\ =10\end{array}$

Calculation of money multiplier for reserve ratio of 20%:

  $\begin{array}{c}\text{Money multiplier}=\frac{1}{R}\\ =\frac{1}{0.2}\\ =5\end{array}$

Calculation of money multiplier for reserve ratio of 25%:

  $\begin{array}{c}\text{Money multiplier}=\frac{1}{R}\\ =\frac{1}{0.25}\\ =4\end{array}$

Calculation of money multiplier for reserve ratio of 50%:

  $\begin{array}{c}\text{Money multiplier}=\frac{1}{R}\\ =\frac{1}{0.5}\\ =2\end{array}$

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.