Finance and Growth

By: Georgina Fourie

Student Number: 201223436

Module Code: PFS3A10

Date: 09 March 2014

ContentInterest and Interest RatesThe difference between interest and interest rates.Terminology.Simple Interest.Compound Interest.

Foreign Exchange RatesCurrent exchange rates.Writing exchange rates as ratios.

The Difference Between Interest and Interest Rates

Interest : This is seen as money in the context of finance and can be seen as two things

1. Interest earned – The reward that a bank or company will pay their clients for depositing or investing money with them.

2. Interest owed – The fee or charge that a person pays for borrowing money

The Difference Between Interest and Interest Rates

Interest Rate – This is the rate at which a person is rewarded for money that has been invested or charged for money that has been borrowed.

Interest rate is usually expressed as

a percentage

The Difference Between Interest and Interest Rates

Example:

Nomsa takes R18 000 student loan from the bank to pay for her studies. The bank is charging her 12%

interest per annum on the loan.

This rate of 12% is the INTEREST RATE.The amount Nomsa has to pay back to the bank

every month is the INTEREST.

TerminologyHire purchase loan repayments are calculated

using simple interest formula on cash price, less deposit.

Monthly repayments are calculated by dividing the accumulated amount by the number of months for the repayment.

Terminology Inflation is the average increase in the price of

goods each year and is given as a percentage.

Population growth is calculated using compound interest formula.

Foreign exchange rate is the price of one currency in terms of another.

Simple Interest

Simple interest is interest that is calculated on the principal or original amount for the length of time for which it is borrowed. Simple interest is due at

the end of the term.

Another word for simple interest is

Hire Purchase

Simple InterestFormula:

A = P(1+n×i)

A Final amount.P Initial/Principle amount.n Number of increases/decreases. i Rate of interest per increase/decrease.

Simple Interest

Example:

Find the final amount if R860 is invested for 3 years at 5% simple interest?

Simple Interest

Solution:

A=? , P=R860 , n=3 years , i=5%

A=P(1+n×i)

A= 860 (1+3×0.05)

A=R989,00c

Simple InterestManipulating the formula to find i

Original formula : A = P(1+n×i)

Manipulated formula:

Simple InterestFor Example:

An investment of R500 increases to R1243 after 2 years. Determine the rate at which simple interest

is being calculated on the investment.

Simple Interest

A = R1243, i = ?, n = 2 years, P = R500

Compound Interest

Compound interest is called ‘interest upon interest’ because it is interest that is being paid on the

original investment as well as on the interest that you have earned previously.

Another word for compound interest is Inflation.

Compound InterestFormula:

A= P(1+i)ⁿ

A Final amount.P Initial/Principle amount.n Number of increases/decreases. i Rate of interest per increase/decrease.

Compound Interest

Compound interest can be calculated:

Annually – Keep original numbers.Half-yearly – i = ÷2 ; n = ×2Quarterly – i = ÷4 ; n = ×4Monthly - i = ÷12 ; n = ×12Weekly - i = ÷52 ; n = ×52Daily – i = ÷365 ; n = ×365

Compound InterestExample:

Jim receives R1000 on his birthday and decides to save it. He can get an interest rate of 4% at the

bank. Interest is compounded annually for 3 years. How much will Jims investment be worth after the 3

years?

Compound InterestSolution:

A=? , P=R1000 , n=3 years , i=4%

A= P(1+i)ⁿ

A= 1000(1+ 0.04)³

A= R1124.86c

Complex ExampleQuestion:

1. Michael invests R3500 in a savings account. The interest rate for the first 4 years is 8% p.a.

compounded monthly, thereafter the interest rate is changed to 9% p.a. compounded half-yearly for the next 5 years. Determine the amount of money that Michael had in his savings account at the end of

this period.

Complex ExampleSolution:

Part A:

A=? , P=R3500 , n=4×12 , i=8%÷12

A= P(1+i)ⁿ

A= 3500(1+ 0.08÷12)

A= R4814.83c

Complex ExampleSolution:

Part B:

A=? , P=R4814.83 , n=5×2 , i=9%÷2

A= P(1+i)ⁿ

A= 4814.83(1+ 0.09÷2)

A= R7477.29c

Therefore Michael had R7477.29c in his savings account

Compound InterestManipulating the formula to get i

Original formula: A= P(1+i)ⁿ

Manipulated formula:

Compound InterestFor Example:

Mpho invests R 30 000 into an account that and after investing for 4 years compound interest he had

R40 146,76c. What was his interest rate if it was compounded annually .

Use the formula:

Compound InterestA = R40 146,76, P= R30 000, i = ?, n = 4

Exchange Rates

Exchange rates refer to the cost of buying currencies from different countries.

A ‘currency’ is the type of money that a country uses to buy and sell goods and

services

Current Exchange Rates

The table below shows the exchange rates of various currencies and what they buy and sell each

currency for at this present time.

Writing Exchange Rates as Ratios

An exchange rate is a ratio that shows the price of one currency in terms of another currency

For example:

Write the following in its simplest ratio if the exchange rate of R6,9363 is equal to $1.00.

R6,9363: $1.00

Writing Exchange Rates as Ratios

Another Example:

Write the following in its simplest ratio if the exchange rate of R6,9363 is equal to $1.00, how many dollars are you able to receive if you have R200.

Reference ListSiyavula (2012). Finance Grade 10. Available

From: http://www.slideshare.net/Siyavula_Education/finance-and-growth?qid=9cccb4a8-91ad-4ec6-b34d-bb54860c4721&v=qf1&b=&from_search=2 (Accessed on 07th March 2014).

Mfuphi, M.(2012). Financial Mathematics. Available From: http://www.slideshare.net/201035224/financial-mathematics?qid=3c4ede27-eafb-48aa-ad8d-b3ff8a7602bc&v=qf1&b=&from_search (Accessed on 07th March 2014).

Reference ListXehgo, V. (2014). Financial Mathematics Simple

and Compound Interest. Available From: http://www.slideshare.net/Vukile/201218457-financial-mathematics?qid=3b8ec53b-8b90-47db-9ef6-1f4b7ec96a87&v=default&b=&from_search=4 ( Accessed on 08th March 2014).

Mbhamali, T.(2014). Mathematics for grade 10-12. Available From: http://www.slideshare.net/Mbhamalitn/financial-mathematics-for-grade-10-11-and-12?qid=3b8ec53b-8b90-47db-9ef6-1f4b7ec96a87&v=default&b=&from_search=7 (Accessed on 08th March 2014).

Reference ListNsimbini, N.(2013). Financial Mathematics Mixed

Problems. Available From: http://www.slideshare.net/Nelisiwepeace/financial-mathematics-mixed-problems?qid=3b8ec53b-8b90-47db-9ef6-1f4b7ec96a87&v=default&b=&from_search=5 (Accessed on 09th March 2014).

Kmwangi, (2009). Financial Mathematics. Available From: http://www.slideshare.net/kmwangi/pow-mathematician-on-wall-street?qid=23c08bed-890f-474f-8b2a-d8cfeef02498&v=qf1&b=&from_search=8 (Accessed on 09th March 2014).