Lecture 02 mathematics of finance w2

Percentages – Index numbers Số chỉ sốAn index number is an economic data figure reflecting price or quantity compared with a standard or base value.. Percentages – Index numbers Số chỉ

Lecture notes on Mathematics for business

VU TUAN ANH, MSA, CMA

I NTERNATIONAL UNIVERSITY, VNU-HCMC, VIETNAM

Lecture 2: Mathematics of Finance

At the end of this section you should be able to:

• Understand what a percentage is.

• Solve problems involving a percentage increase or decrease.

• Write down scale factors (hệ số tỉ lệ) associated with percentage changes.

• Work out overall percentage changes.

• Calculate and interpret index numbers.

• Adjust value data for inflation

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Percentages

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Percentages – Index numbers (Số chỉ số)

An index number is an economic data figure reflecting price or quantity

compared with a standard or base value The base usually equals 100 and the index number is usually expressed as 100 times the ratio to the base value.

Index number = scale factor from base year × 100

Time series is simply a series of data points ordered in time.

Percentages – Index numbers (Số chỉ số)

Example:

Table 3.1 shows the values of household spending (in billions of dollars) during a

5-year period Calculate the index numbers when 2011 is taken as the base year.

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Percentages – Index numbers (Số chỉ số)

Examples:

Percentages – Index numbers (Số chỉ số)

Examples:

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Percentages – Index numbers (Số chỉ số)

• Passche index is an index number for groups of

data weighted by the quantities used in the

• Laspeyres index is an index number for groups

of data which are weighted by the quantities

Percentages – Index numbers (Số chỉ số)

Percentages – Index numbers (Số chỉ số)

Solution:

So, the Laspeyres index w.r.t the base year of 2014 is

Percentages – Index numbers (Số chỉ số)

Percentages – Inflation (Lạm phát)

Inflation means that the general level of prices is going up, the opposite

bread) and services (like getting a haircut at the hairdresser's).

Nominal data are the original, raw data such as those listed in tables in the

previous subsection

Real data are the values that have been adjusted to take inflation into account

Percentages – Inflation (Lạm phát)

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Percentages – Inflation (Lạm phát)

Percentages – Inflation (Lạm phát)

Examples:

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Percentages – Inflation (Lạm phát)

Examples:

Percentages – Inflation (Lạm phát) – Key

Terms

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Simple interest (lãi đơn)– Compound

interest (lãi kép)

At the end of this section you should be able to:

▪ Understand the difference between simple and compound

Simple interest (lãi đơn) – Compound

Simple interest (lãi đơn)– Compound interest (lãi kép)

❑ Interest: time value of money

❑ Simple interest: “interest is constant” over each period

If you save P = $500 into a bank account and earn r% = 10% interest (per year) with simple interest, then the interest each year is $500 x 10% = $50

➢ Then the amount of money after n years is S = P(1 + nr/100)

❑ Compound interest: “interest over interest” phenomenon

Compound interest is the calculation of interest based on the principal AND accumulated interest

- Using the prior example, if you have P=$500 and earn r% = 10% interest (per year) compounded yearly , how would you calculate the interest in the second year using compound interest

Simple interest (lãi đơn)– Compound interest (lãi kép)

Note that the interest can be compounded annually, semi-annually, monthly, weekly, daily, every minute, every second…

Let P = Principal value, r% = interest rate per year , the interest is

compounded every period, there are k periods per year, n = the

number of years.

At the end of the n th year, the future value is: S = P(1 + r/(100*k)) kn

Continuously compounded interest : S = Pe rn/100 ; e = 2.718281828459

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Simple interest (lãi đơn)– Compound

interest (lãi kép)

Examples :

Simple interest (lãi đơn)– Compound

interest (lãi kép) – DO IT !

Examples :

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Simple interest (lãi đơn)– Compound

interest (lãi kép)

Examples :

Simple interest (lãi đơn)– Compound

interest (lãi kép)

Examples :

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Simple interest (lãi đơn)– Compound interest

(lãi kép) – Annual Percentage Rate (APR)

Annual percentage rate (APR) is the rate of interest, which when compounded annually,

produces the same yield as the nominal of interest.

Annual percentage rate (APR) is the annualized interest rate on a loan or investment

which does take into account for the effect of compounding !

The phrase ‘annual equivalent rate’ (AER) is frequently used when applied to savings.

Note: APR is also the annual interest rate, for the same principal P to produce the same

future value S after 1 year.

Then after one year, S = P(1 + APR) and S = P(1 + r/(100*k)) k >>>:

Simple interest (lãi đơn)– Compound interest

(lãi kép) – Annual Percentage Rate (APR)

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Simple interest (lãi đơn)– Compound interest

(lãi kép) – Annual Percentage Rate (APR)

DO IT !

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DO IT !

Simple interest (lãi đơn)– Compound interest

(lãi kép) – Annual Percentage Rate (APR) – DO

IT !

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Please check on blackboard for suggested exercises !