IB Math Studies – Topic 8

Financial Mathematics

IB Course Guide Description

Currency Conversion

• Exchange rates show the relationship between the values of currencies. They change constantly. – The exchange rates in any country are usually given as the

amount of foreign currency equal to one unit of the local currency.

• People by and sell international currency– Selling:

• Foreign currency bought = other currency sold x selling exchange rate

– Buying:• Currency bought = (foreign currency sold) / (buying exchange rate)

What is Commission?• Banks and other currency traders earn a

commission for exchanging currency.• commission rate between 0.5% to 3%• a ‘flat fee’• no commission, but worse exchange rates

Simple Interest

100

CrnI

C = capital

r = simple interest rate / per year / decimal

n = number of time periods (in years)

I = interest

1) If $2000 is borrowed at a 8% p.a. for 3 years, the interest payable for 1 year is 8% of $2000, therefore it is $2000 x 0.08.

So, for 3 years it would be ($2000 x 0.08)x3

Compound Interest

• Compound interest is a method of calculating interest in which the interest is added to the principal each period so that the principal continues to grow throughout the life of the loan or investment.

This will be there for you!

How to solve using your CALCULATOR

N: The number of compounding periods. This will always be a positive integer.I%: This is the 'nominal rate' for an investment, annuity or loan. This will always be a positive integer. Write the percent form, not the fraction or decimal form of a percent. PV: The 'present value' of an investment, loan or annuity. This number can be positive or negative. if the number is positive, then it indicated money we collected as in a loan. If the number is negative, then it represents money we paid out, as in an investment or loan where we are the lender. FV: The 'future value' of an investment, annuity or loan after N compounding periods have passed. This value will be positive or negative depending on the signs of PV and PMT. P/Y: This value represents the number of payments per year for annuities and loans. This must be a positive integers!C/Y: This represents the number of compounding periods per year. This must be a positive integers!

Depreciation

• Depreciation is the loss in value of an item over a certain period of time.

Tables: Loan and Repayments

• Financial table: It is often used to give information about investment or loan repayment which enable interest amount to be calculated without using formulae.

Investment• An investment is an amount of money that we loan to

someone. • The majority of time this is done through compound

interest, where the compound interest is added to the investments.

Inflation

• The increase in prices of goods and wages.• If inflation rate is constant over a number of years,

we can use compounded interest.

• We calculate the effect of inflation, we treat the original price in the past as the principal and the inflation rate as an interest rate. From then we use the compound interest to calculate the effect of the inflation rate on the price.

•

Bibliography

• "Using the TVM." Error. Web. 23 Apr. 2012. <http://staff.argyll.epsb.ca/jreed/calculator/ti83p/TMV.htm>.– Slide 9