5-1 Copyright 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e Chapter 5 Simple

5-1Copyright 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e

Chapter 5

Simple interest

Introductory Mathematics & Statistics for Business


Learning Objectives

• Understand the effect of inflation on interest rate levels

• Perform calculations involving simple interest

• Manipulate the simple interest formula

• Distinguish between, and calculate, flat and effective rates of interest

• Estimate the effective rate of interest


5.1 Introduction• Interest denotes any income received from capital that has

been invested, or the amount of money paid for the use of borrowed money

• The actual amount of money that has been lent or invested, or the current balance of the original amount, is called the principal (or capital).

• The amount of money received as interest depends on three factors:

1. The principal or capital

2. The rate of interest

3. The duration of the debt or investment


Introduction (cont…)

• The amount of a loan or investment before interest is added on (or a discount is taken off) is called the face value

• The actual interest (or return) expressed as a percentage of the price paid is called the yield.

• The actual rate of interest charged by lending institutions depends on many factors, including – current and expected inflation rates, – competition between financial institutions, – the size of Australia’s budget deficit– the amount of the principal



• The effect of inflation on the level of interest rates

– According to monetary theory, price levels in general will rise if the money supply grows more quickly than the total output of the economy.

– Inflation may be defined as persistent increase in the general level of prices and is normally accompanied by high interest rates

– Those who borrow money are able to pay the higher interest rate if inflation enables them to raise their selling price to pay for it. In this way, borrowers themselves are helping to create an inflationary spiral in which inflation and interest rates continually push each other higher.



• One of the factors affecting mortgage rates of interest is the cost of goods and services. That is, inflation is going to reduce the value of the money and mortgage rates will rise

• Many factors affect interest rates, including– high unemployment rates – overseas interest rates, – balance of payments figures, – deregulation of the financial system, – the amount held in deposits and especially – government policy


5.2 Calculation of simple interest

• Simple interest, is the interest calculated, based on the original principal during the entire period at the stated rate of interest.

• Given

P = principal

R = rate of interest

T = time (in years)

I = total simple interest

S = amount or maturity value of the principal

• Simple interest:

TRPI


Calculation of simple interest (cont…)

• The maturity value of the principal is:

• What amount of principal will give a certain maturity value.

• When P is calculated from S, the value of P is called the present value of S or the discounted value of S.

RT1PS

RT1

SP



Example

Calculate the simple interest earned on $15 000 deposited at a rate of 1.5% per annum for a period of 4 years and 3 months

Solution

Hence, the total simple interest earned is $956.25.

25.956$

25.4015.01500$

TRPISo

25.4THere


Calculation of simple interest (cont…)Example

A bank customer invests $5000 for 18 months at a simple interest rate of 9.5% per annum. Find the maturity value of the principal

SolutionP= $5000, R = 0.095 and T = 1.5

Hence, the maturity value of the principal is $5712.50

50.5712$

1425.15000$

5.1095.015000$

RT1PS



ExampleAn investor wishes to have an amount of $4000 on maturity in 5 years time. A simple interest rate of 12.0% per annum is offered. How much money should be invested now in order to achieve this aim?

SolutionS= $4000, R = 0.12 and T = 5

Hence, the investor should invest $2500 now in order to have $4000 at the end of 5 years.

2500$512.01

4000$RT1

SP



• Minimum Monthly Balance

– Many financial institutions in Australia pay simple interest based on the minimum monthly balance in an account each month.

– That is, if a sum of money is deposited and withdrawn during the same month, it will not attract any interest.

Use

Where

P = minimum monthly balance

R = rate

12

1T

TRPI



ExampleA customer opens a savings account on 15 October 2009 with a sum of $1000. The bank pays simple interest on the account at a rate of 2.5% per annum based on the minimum monthly balance. Calculate the interest due for November

Solution

Hence the interest due for November is $2.08

08.2$12

1025.01000$

PRTI


5.3 Effective rate of interest

• This is an interest rate that is always based on the original principal, even though the amount of the loan is reducing.

• For every flat rate of interest their will be an equivalent effective rate. Its approximate value is given by:

Where: E = effective rateR = flat rate

N = number of repayments

1 N

RN 2 E


Effective rate of interest (cont…)Example

A customer takes out a $15 000 personal loan from the bank to be repaid monthly over 5 years. The bank has quoted a flat rate of interest of 9.5%. Calculate the equivalent effective rate of interest

Solution

Hence, the effective rate of interest is 18.69%.

095.0R,60125N

1869.0160

095.06021N

RN2E


Effective rate of interest (cont…)

To find the flat rate of interest that is equivalent to a given effective rate

Where: E = effective rate

R = flat rate

N = number of repayments

N2

E1NR


Effective rate of interest (cont…)Example

A credit union is offering home equity loans to be repaid over 20 years with monthly repayments and an effective rate of interest of 11.5%. Calculate the equivalent flat rate of interest

Solution

Hence, the equivalent flat rate of interest is 5.774%.

115.0E,2401220N

05774.02402

115.01240N2

E1NR


Summary

• We looked at understanding the effect of inflation on interest rate levels

• We perform calculations involving simple interest

• Also looked at how to manipulate the simple interest formula

• Looked at the difference between, and calculate, flat and effective rates of interest

• Lastly estimated the effective rate of interest

Documents

5-1 Copyright 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e Chapter 5 Simple