Textbook

Introduction

1. Goals and decisions of an organization

2. The market system

3. The domestic economy

4. Macroeconomics – The international economy

5. Macroeconomics – Index numbers

6. Introduction to the financial context of business entities

6.1 Financial markets

6.2 Characteristics of financial instruments

6.3 Financial instruments

6.4 Short-term instruments

6.5 Interest rates

7. Foreign currencies

8. Investment appraisal

9. Summarizing and analyzing data

10. Inter-relationships between variables

11. Time series model

Wrapping up

6.5 Interest rates

CGMA BA1

6. Introduction to the financial context of business entities

Our CGMA course is currently in development and is a work-in-progress.

Interest rates

3 min read

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Real and money rate/nominal rate

These ideas come up often in finance, so it’s worth getting the basics clear early.

Nominal rate of interest

The nominal (money) interest rate is the stated interest rate you see quoted by banks and lenders. It includes the effect of inflation.

Real rate of interest

The real interest rate is the interest rate after removing the effect of inflation. It reflects the change in purchasing power.

How do you calculate the real rate when given the nominal rate of interest?

You use the relationship between the nominal rate and inflation.

Real interest rate formula

$\frac{1 + m}{1 + i}$

Where:

$m$ = money (nominal) rate of interest
$i$ = inflation rate

This formula gives you the real interest factor. To get the real interest rate, you subtract $1$ from the factor.

If the question asks you to calculate the money rate of interest when the real interest rate is given, use the same relationship and rearrange as needed.

Example 3

KTA has a money (nominal) interest rate of $12%$ from the bank on an annual basis. The annual inflation rate is $5%$ . What is the real interest rate that KTA is paying to the bank?

Solution

(spoiler)

First, convert the percentages to decimals:

$12% = 0.12 5% = 0.05$

Now apply the formula:

$Real interest factor = \frac{1 + 0.12}{1 + 0.05} = \frac{1.12}{1.05} = 1.0667$

Subtract $1$ to isolate the real rate:

$1.0667 - 1 = 0.0667$

Convert back to a percentage:

$0.0667 \times 100% = 6.67%$

So, the real interest rate is $6.67%$ .

If the question instead requires recalculating the money rate of interest, multiply the real interest factor by inflation:

$(1 + m) = 1.0667 \times 1.05 = 1.12$

Subtract $1$ and convert to a percentage:

$(1.12 - 1) \times 100% = 12%$

Functions of a central bank/reserve bank of a country

Supervision of the money supply and the banking system of a country

A central bank manages the country’s money supply and supports the stability of the banking system.

One way it influences the economy is by changing interest rates, especially the base rate (the rate at which commercial banks borrow from the central bank). The basic chain works like this:

If the base rate increases, commercial banks face higher borrowing costs.
Commercial banks typically pass this on by increasing the interest rates they charge customers.
If the base rate decreases, commercial banks can usually reduce the rates they charge customers.

You’ll often see base rate changes reported in basis points:

100 base points = 1%

So, if a central bank increases the base rate by 100 base points, it has increased the rate by 1%. You can interpret other changes using the same conversion.

This process is known as quantitative easing.

Banker to the banks

The central bank supplies money to commercial banks. This supports everyday banking activity, including:

cash withdrawals from ATMs
electronic transfers and payments

Banker to the government

The central bank also acts as the government’s bank. For example:

The government may borrow directly from the central bank for large projects.
When the government issues bonds, it issues them through the central bank.

Lender of last resort

As a lender of last resort, the central bank provides emergency funding when other borrowing options aren’t available. This can apply to:

commercial banks that need urgent liquidity
the government, especially when it needs large amounts of funding and repayment may take longer

Nominal rate of interest

Stated (quoted) interest rate by banks/lenders
Includes effect of inflation

Real rate of interest

Interest rate adjusted for inflation
Reflects change in purchasing power

Real interest rate formula

Real interest factor: $\frac{1 + m}{1 + i}$
- $m$ = nominal (money) rate
- $i$ = inflation rate
Real interest rate = real interest factor $- 1$
Rearranged formula used to solve for any variable (nominal, real, or inflation rate)

Functions of a central bank/reserve bank

Supervision of money supply and banking system

Manages national money supply
Sets base rate (influences commercial bank rates)
Base rate changes measured in basis points (100 basis points = 1%)
Quantitative easing: process of influencing economy via interest rates

Banker to the banks

Supplies money to commercial banks
Supports cash withdrawals, electronic payments

Banker to the government

Handles government borrowing and bond issuance
Acts as government’s primary bank

Lender of last resort

Provides emergency funding to commercial banks and government
Ensures financial system stability during crises

Next | 7.1 Introduction

Interest rates

Real and money rate/nominal rate

These ideas come up often in finance, so it’s worth getting the basics clear early.

Nominal rate of interest

The nominal (money) interest rate is the stated interest rate you see quoted by banks and lenders. It includes the effect of inflation.

Real rate of interest

The real interest rate is the interest rate after removing the effect of inflation. It reflects the change in purchasing power.

How do you calculate the real rate when given the nominal rate of interest?

You use the relationship between the nominal rate and inflation.

Real interest rate formula

$\frac{1 + m}{1 + i}$

Where:

$m$ = money (nominal) rate of interest
$i$ = inflation rate

This formula gives you the real interest factor. To get the real interest rate, you subtract $1$ from the factor.

If the question asks you to calculate the money rate of interest when the real interest rate is given, use the same relationship and rearrange as needed.

Example 3

KTA has a money (nominal) interest rate of $12%$ from the bank on an annual basis. The annual inflation rate is $5%$ . What is the real interest rate that KTA is paying to the bank?

Solution

(spoiler)

First, convert the percentages to decimals:

$12% = 0.12 5% = 0.05$

Now apply the formula:

$Real interest factor = \frac{1 + 0.12}{1 + 0.05} = \frac{1.12}{1.05} = 1.0667$

Subtract $1$ to isolate the real rate:

$1.0667 - 1 = 0.0667$

Convert back to a percentage:

$0.0667 \times 100% = 6.67%$

So, the real interest rate is $6.67%$ .

If the question instead requires recalculating the money rate of interest, multiply the real interest factor by inflation:

$(1 + m) = 1.0667 \times 1.05 = 1.12$

Subtract $1$ and convert to a percentage:

$(1.12 - 1) \times 100% = 12%$

Functions of a central bank/reserve bank of a country

Supervision of the money supply and the banking system of a country

A central bank manages the country’s money supply and supports the stability of the banking system.

One way it influences the economy is by changing interest rates, especially the base rate (the rate at which commercial banks borrow from the central bank). The basic chain works like this:

If the base rate increases, commercial banks face higher borrowing costs.
Commercial banks typically pass this on by increasing the interest rates they charge customers.
If the base rate decreases, commercial banks can usually reduce the rates they charge customers.

You’ll often see base rate changes reported in basis points:

100 base points = 1%

So, if a central bank increases the base rate by 100 base points, it has increased the rate by 1%. You can interpret other changes using the same conversion.

This process is known as quantitative easing.

Banker to the banks

The central bank supplies money to commercial banks. This supports everyday banking activity, including:

cash withdrawals from ATMs
electronic transfers and payments

Banker to the government

The central bank also acts as the government’s bank. For example:

The government may borrow directly from the central bank for large projects.
When the government issues bonds, it issues them through the central bank.

Lender of last resort

As a lender of last resort, the central bank provides emergency funding when other borrowing options aren’t available. This can apply to:

commercial banks that need urgent liquidity
the government, especially when it needs large amounts of funding and repayment may take longer

CGMA BA1

6. Introduction to the financial context of business entities

Our CGMA course is currently in development and is a work-in-progress.

Interest rates

3 min read

Font

Discuss

Feedback

Real and money rate/nominal rate

These ideas come up often in finance, so it’s worth getting the basics clear early.

Nominal rate of interest

The nominal (money) interest rate is the stated interest rate you see quoted by banks and lenders. It includes the effect of inflation.

Real rate of interest

The real interest rate is the interest rate after removing the effect of inflation. It reflects the change in purchasing power.

How do you calculate the real rate when given the nominal rate of interest?

You use the relationship between the nominal rate and inflation.

Real interest rate formula

$\frac{1 + m}{1 + i}$

Where:

$m$ = money (nominal) rate of interest
$i$ = inflation rate

This formula gives you the real interest factor. To get the real interest rate, you subtract $1$ from the factor.

If the question asks you to calculate the money rate of interest when the real interest rate is given, use the same relationship and rearrange as needed.

Example 3

KTA has a money (nominal) interest rate of $12%$ from the bank on an annual basis. The annual inflation rate is $5%$ . What is the real interest rate that KTA is paying to the bank?

Solution

(spoiler)

First, convert the percentages to decimals:

$12% = 0.12 5% = 0.05$

Now apply the formula:

$Real interest factor = \frac{1 + 0.12}{1 + 0.05} = \frac{1.12}{1.05} = 1.0667$

Subtract $1$ to isolate the real rate:

$1.0667 - 1 = 0.0667$

Convert back to a percentage:

$0.0667 \times 100% = 6.67%$

So, the real interest rate is $6.67%$ .

If the question instead requires recalculating the money rate of interest, multiply the real interest factor by inflation:

$(1 + m) = 1.0667 \times 1.05 = 1.12$

Subtract $1$ and convert to a percentage:

$(1.12 - 1) \times 100% = 12%$

Functions of a central bank/reserve bank of a country

Supervision of the money supply and the banking system of a country

A central bank manages the country’s money supply and supports the stability of the banking system.

One way it influences the economy is by changing interest rates, especially the base rate (the rate at which commercial banks borrow from the central bank). The basic chain works like this:

If the base rate increases, commercial banks face higher borrowing costs.
Commercial banks typically pass this on by increasing the interest rates they charge customers.
If the base rate decreases, commercial banks can usually reduce the rates they charge customers.

You’ll often see base rate changes reported in basis points:

100 base points = 1%

So, if a central bank increases the base rate by 100 base points, it has increased the rate by 1%. You can interpret other changes using the same conversion.

This process is known as quantitative easing.

Banker to the banks

The central bank supplies money to commercial banks. This supports everyday banking activity, including:

cash withdrawals from ATMs
electronic transfers and payments

Banker to the government

The central bank also acts as the government’s bank. For example:

The government may borrow directly from the central bank for large projects.
When the government issues bonds, it issues them through the central bank.

Lender of last resort

As a lender of last resort, the central bank provides emergency funding when other borrowing options aren’t available. This can apply to:

commercial banks that need urgent liquidity
the government, especially when it needs large amounts of funding and repayment may take longer

Nominal rate of interest

Stated (quoted) interest rate by banks/lenders
Includes effect of inflation

Real rate of interest

Interest rate adjusted for inflation
Reflects change in purchasing power

Real interest rate formula

Real interest factor: $\frac{1 + m}{1 + i}$
- $m$ = nominal (money) rate
- $i$ = inflation rate
Real interest rate = real interest factor $- 1$
Rearranged formula used to solve for any variable (nominal, real, or inflation rate)

Functions of a central bank/reserve bank

Supervision of money supply and banking system

Manages national money supply
Sets base rate (influences commercial bank rates)
Base rate changes measured in basis points (100 basis points = 1%)
Quantitative easing: process of influencing economy via interest rates

Banker to the banks

Supplies money to commercial banks
Supports cash withdrawals, electronic payments

Banker to the government

Handles government borrowing and bond issuance
Acts as government’s primary bank

Lender of last resort

Provides emergency funding to commercial banks and government
Ensures financial system stability during crises

Next | 7.1 Introduction

Interest rates

Real and money rate/nominal rate

These ideas come up often in finance, so it’s worth getting the basics clear early.

Nominal rate of interest

The nominal (money) interest rate is the stated interest rate you see quoted by banks and lenders. It includes the effect of inflation.

Real rate of interest

The real interest rate is the interest rate after removing the effect of inflation. It reflects the change in purchasing power.

How do you calculate the real rate when given the nominal rate of interest?

You use the relationship between the nominal rate and inflation.

Real interest rate formula

$\frac{1 + m}{1 + i}$

Where:

$m$ = money (nominal) rate of interest
$i$ = inflation rate

This formula gives you the real interest factor. To get the real interest rate, you subtract $1$ from the factor.

If the question asks you to calculate the money rate of interest when the real interest rate is given, use the same relationship and rearrange as needed.

Example 3

KTA has a money (nominal) interest rate of $12%$ from the bank on an annual basis. The annual inflation rate is $5%$ . What is the real interest rate that KTA is paying to the bank?

Solution

(spoiler)

First, convert the percentages to decimals:

$12% = 0.12 5% = 0.05$

Now apply the formula:

$Real interest factor = \frac{1 + 0.12}{1 + 0.05} = \frac{1.12}{1.05} = 1.0667$

Subtract $1$ to isolate the real rate:

$1.0667 - 1 = 0.0667$

Convert back to a percentage:

$0.0667 \times 100% = 6.67%$

So, the real interest rate is $6.67%$ .

If the question instead requires recalculating the money rate of interest, multiply the real interest factor by inflation:

$(1 + m) = 1.0667 \times 1.05 = 1.12$

Subtract $1$ and convert to a percentage:

$(1.12 - 1) \times 100% = 12%$

Functions of a central bank/reserve bank of a country

Supervision of the money supply and the banking system of a country

A central bank manages the country’s money supply and supports the stability of the banking system.

One way it influences the economy is by changing interest rates, especially the base rate (the rate at which commercial banks borrow from the central bank). The basic chain works like this:

If the base rate increases, commercial banks face higher borrowing costs.
Commercial banks typically pass this on by increasing the interest rates they charge customers.
If the base rate decreases, commercial banks can usually reduce the rates they charge customers.

You’ll often see base rate changes reported in basis points:

100 base points = 1%

So, if a central bank increases the base rate by 100 base points, it has increased the rate by 1%. You can interpret other changes using the same conversion.

This process is known as quantitative easing.

Banker to the banks

The central bank supplies money to commercial banks. This supports everyday banking activity, including:

cash withdrawals from ATMs
electronic transfers and payments

Banker to the government

The central bank also acts as the government’s bank. For example:

The government may borrow directly from the central bank for large projects.
When the government issues bonds, it issues them through the central bank.

Lender of last resort

As a lender of last resort, the central bank provides emergency funding when other borrowing options aren’t available. This can apply to:

commercial banks that need urgent liquidity
the government, especially when it needs large amounts of funding and repayment may take longer