COMPLETE summary of grade 12 financial maths

Financial Mathematics

Revision from Grades 10 and 11

 Simple Interest: A  P1 i.n 
 Compound Interest: A  P1  i  where:
n




P = the principal amount.
A = final amount including interest.
i = interest rate per time period
n = number of time periods.

 Nominal and Effective interest rates:

𝑚 = 12 Monthly
Semi-Annually
m
 inom
 𝑚=2
1  i eff  1  
 m  𝑚=4 Quarterly
𝑚 = 365 Daily


 Straight Line Depreciation: A  P1  i.n 
 Reducing Balance Depreciation: A  P1  i 
n




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,Time Lines revision

Examples

1) Amahle deposits R75 000 into a savings account paying 12% per annum
compounded monthly. She wants to buy a car in 3 years’ time.
a) Calculate how much money will be available to her in three years’ time, if she
makes a further deposit of R25 000 into her account one year after her
first deposit.
b) Amahle then buys the car for the amount saved after three years. She
drives the car for four years and then sells the car. Suppose that after four
years of reducing balance depreciation, the car is worth one quarter of its
original value. Calculate the rate of depreciation as a percentage.




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, 2) Stephen invests R40 000 at 15% per annum compounded quarterly for a period
of 10 years.
a) Convert the nominal interest rate of 15% per annum compounded quarterly
to the effective rate (annual).
b) Now use the annual effective rate to calculate the future value of the
investment after 10 years.




3) Siyabonga deposits R150 000 into a five year savings account. Two years later,
he withdraws R40 000. Calculate the future value of his investment if the
interest rate for the first three years is 16% per annum compounded monthly
and 16% compounded half-yearly for the remaining two years.




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