Mathematics literacy G10,11,12 Assignment and online Extra lessons

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🚨Grade 12 Final Examination Time table 🚨🏌️

⚠️ October/November 2022⚠️

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🚨How to calculate interest continue 👇🏻

⚠️We have seen that for a medium term liability, the interest is worked out over the entire
period before it is broken up into monthly repayments. A home loan works differently.
Every month interest is worked out for that month. The repayment is then subtracted
from the total and a new interest amount is worked out for the next month. The
payment is usually higher than the interest amount, which means that part of the
capital amount will also be paid. The interest calculated for the next month is
calculated on the amount of capital outstanding after the previous payment. The
following example illustrates this concept.
E.g.
Bill buys a house for R500,000.00 at an interest rate of 9,5 per year payable monthly.
Bill estimates that he can afford to pay an instalment of R6,000.00 per month to pay off
the loan.
The interest rate is 9,5% per year which means that we have to work out one twelfth of
that per month. 9,5/12 = 0,79%. So the interest rate per month is 0,79%.
Month 1: The interest part of Bill‟s first monthly payment is P.r.n
500000 x 0,0079 x 1 = 3950
Bill pays R6 000,00, so the capital he pays toward the loan is
6000 – 3950 = 2050.
The value of the loan at the end of that month is (500000 – 2050)
R497,950.00

Month 2: We have to consider the value of the loan at the end of the last interest
period to work out the new interest value (P is now R497 950,00 in stead
of R500,000.00)
497950 x 0,0079 x 1 = 3933,81
Bill pays R6,000.00, so the capital he pays toward the loan is
6000 – 3933,81 = 2066,19
The value of the loan at the end of this month is (497950 – 2066,19)
R495,883.81
Can you see that he pays more of the capital off in the second month compared to the
first month?

Te end🏌️

🚨 How to calculate interest continue 👇🏻

⚠️The interest rate is mostly dependent on the prime-lending rate. This is linked to the
interest rate at which banks borrow their money from the South African Reserve Bank.
The banks add a percentage to the prime-lending rate to cover their own finance
costs.
In September 2006, the prime-lending rate was 11,5%. Most first time buyers had to
pay „prime + 2‟. This means that the interest rate for a car loan was 13,5% per annum.
E.g.
Complete the following table to illustrate the repayment values for a car that costs
R100,000.00 over different periods. The interest rate is 13,5% compounded monthly.

🏓

🧹1. Calculate the value of the interest you pay for each payment option.
CASH: A – P = 100 000 – 100 000 = 0
No interest has to be paid
12 MONTHS: A – P = 114 030 – 100 000 = 14 030
R14 030 must be paid as interest
24 MONTHS: A – P = 130 030 – 100 000 = 30 030
R30 030 must be paid as interest
36 MONTHS: A – P = 148 270 – 100 000 = 48 270
R48 270 must be paid as interest
48 MONTHS: A – P = 169 070 – 100 000 = 69 070
R69 070 must be paid as interest
60 MONTHS: A – P = 192 780 – 100 000 = 92 780
R92 780 must be paid as interest
2. What is the monthly payment for the car if a loan has been taken over 60 months?
The total amount to be repaid is R192,780.
There are 60 payments.
So:
19278060  3213
This means that the monthly payment will be R3,213.00 per month.
Note: As you can see, if R3,213.00 is saved up per month before you bought the car
in the example, you would have had to save for

100000 3213 31.12
, i.e. 32 months,
to afford the car. You would have saved 28 months worth of payments. Essentially this
means that on a 60-month loan you will pay interest for 28 of the 60 months.
3.2. BUYING A HOUSE
Since all loans have different terms and conditions, it might be wise to look at a home
loan as well. Owning a house is often considered a long-term liability. This means that
most people do not have the means to pay cash for a house; they are required to pay
it off.
Banks allow for an interest amount of less than the prime rate because the amounts
are large and the term is much longer than that for a car (often 20-25 years).

Continue 👆🏻

🚨How to calculate interest continue 👇🏻

⚠️2.2.2 Interest Charged Quarterly, Monthly or Daily
E.g.
Compare the following three scenarios (A, B and C).
A: Mike invests R5,000.00 at 8% interest compounded annually for a period of 5 years.
Since the interest is compounded annually (yearly), we use the interest rate and the
number of periods as they have been given. This means that the r in our formula is
8% and the n is 5.
The calculation looks as follows:
A = P (1 + r)n
A = 5000(1 + 0.08)5
A = R7,346.64
The interest amount:
CI = A – P
CI = 7346,64 – 5000
CI = R2,346.64
B: Mike invests R5,000.00 at 8% interest per annum compounded quarterly for a period
of 5 years. Before we use the formula, we have to adapt the interest rate to the
period it is being compounded in.
1 year = 8%
1 quarter = 2%
1 year has four quarters, so 5 years has 20 quarters
This means that the r in our formula becomes 2% and the n becomes 20.

🧹The calculation looks as follows:
A = P (1 + r)n
A = 5000(1 + 0.02)20
A = R7,429.74
The interest amount:
CI = A – P
CI = 7429,74 – 5000
CI = R2,429.74
C: Mike invests R5,000.00 at 8% interest per annum compounded monthly for a period
of 5 years. Before we use the formula, we have to adapt the interest rate to the
period it is being compounded in.
1 year = 8%
1 month = 0,7%
1 year has twelve months, so 5 years has 60 months
This means that the r in our formula is 0,7% and the n becomes 60.
The calculation looks as follows:
A = P (1 + r)n
A = 5000(1 + 0.007)60
A = R7,598.68
The interest amount:
CI = A – P
CI = 7598,68 – 5000
CI = R2,598.68
ANSWER: This means that option C is the best. Mike is investing not borrowing, so
he would like to have the highest return possible.
3. PRACTICAL EXAMPLES
3.1. BUYING A CAR
When you buy a car, you are required to make financial decisions before the bank
grants you a loan. You must decide if you are going to buy the car cash or whether
you are going to pay it off.Most banks offer the following terms: 12 months, 24
months, 36 months, 48 months or 60 months. (A car is considered to be a medium
term liability, so the bank will not finance it over a period extending five years.)

Continue 👆🏻

🚨How to calculate interest continue 👇🏻

Note: End value of investment = initial loan amount (1 + interest rate x number of
payment intervals) = R1 800.00 (end value of the investment)
2.2. COMPOUND INTEREST
Compound interest differs from simple interest in such a way that we no longer have
the same interest amount every period. We have an interest amount that increases
every period. The reason for this is that we no longer earn interest only on the initial
amount invested but on the interest earned in each of the previous periods as well.
This means that the investment amount, which we use to calculate periodic interest,
constantly changes.
The formula for compound interest differs from the simple interest formula in such a
way that the period is no longer multiplied by the interest rate. It now becomes the
exponent. Thus the compound interest formula calculates the total value of the loan or
investment. The formula is set up as follows:
A = P (1 + r)n
Where,
 A is the total value of the investment or loan at the end of the period
 P is the initial amount invested or borrowed
 r is the interest rate for the payment interval
 n is the number of payment intervals over the total period of the loan or
investment
To isolate the interest amount, we must subtract the initial investment amount from the
total value of the investment. Thus we use the following formula to calculate the
interest value:
CI = A - P
2.2.1. Interest Charged Annually
E.g.
Mike invests R5,000.00 at 10% interest compounded annually.
The interest calculation for the first year of the investment is as follows:
A = P (1 + r)n
A = 5000(1 + 0.10)1
A = R5,500
The interest amount:
CI = A – P
CI = 5500 – 5000
CI = R500

The interest in the second year is based on the initial investment value as well as
the interest earned in the previous periods. The calculation is as follows:
A = P (1 + r)n
A = 5000(1 + 0.10)2
A = R6,050
The interest amount:
CI = A – P
CI = 5500 – 5000
CI = R500

The interest in the second year is based on the initial investment value as well as
the interest earned in the previous periods. The calculation is as follows:
A = P (1 + r)n
A = 5000(1 + 0.10)2
A = R6,050
The interest amount:
CI = A – P
CI = 6050 – 5000
CI = R1,050
Since the interest in the first year was R500.00, it follows that the interest earned in the
second year was R550.00.

Continue 👆🏻

🚨Notes 🚨How to calculate interest

⚠️1. INTRODUCTION
Whenever a person buys something on credit, they are charged interest. Interest is a
fee that is added to the actual value of a product for the convenience of receiving cash
from an institution. There are two types of interest; simple and compound.

🏌️2. INTEREST RATES:
Whenever a person buys something on credit, they are charged interest. Interest is a
fee that is added to the actual value of a product for the convenience of receiving cash
from an institution. This means if you borrow money from a bank, you will have to pay
the actual value of the loan plus an interest fee.
There are two types of interest; simple and compound:
 Simple interest is calculated only on the actual, initial value of the amount
borrowed.
 Compound interest is calculated on the actual, initial value plus interest on the
interest at a specific point in time.

🏌️2.1. SIMPLE INTEREST:
Simple interest is visually interpreted as straight-line growth. This means that for
each equally spaced payment interval, the interest is accrued at the same. The value
of the interest is calculated using the original amount invested or borrowed.
The formula for calculating simple interest is:
A = P (1 + r . n)
= P + P . r . n
Where,
 A is the total value of the investment or loan at the end of the period
 P is the initial amount invested or borrowed
 r is the interest rate for the payment interval
 n is the number of payment intervals over the total period of the loan or
investment
If we wish to calculate only the interest amount accrued over the entire period, we
use the following formula where SI = Simple interest: SI = P.r.n
Note: This formula does not include the money invested/borrowed. It is only the value
of the interest.

Interest is not only calculated on a yearly basis; it may also be calculated on a
quarterly, monthly, half-yearly or daily basis. If the payment interval changes, we have
to adjust

To continue 👆🏻

🚨What is speed?
Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.

🏌️The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

👇🏻Rearranging the formula
The formula speed = distance ÷ time can be rearranged, just like any other equation.

🧙‍♀️The formula can be rearranged in three ways:

speed = distance ÷ time

distance = speed × time

time = distance ÷ speed

🧹To calculate one of the variables (speed, distance or time) we need the other two.

⚠️For example, to find the time taken to make a journey, we need the length of the journey and the speed of travel.

🚨Calculate the range
The formula to calculate the range is:

⚠️Formula to find the range
R = range
H = highest value
L = lowest value
The range is the easiest measure of variability to calculate. To find the range, follow these steps:

🧙‍♀️Order all values in your data set from low to high.
Subtract the lowest value from the highest value.
This process is the same regardless of whether your values are positive or negative, or whole numbers or fractions

🧹Range example
Your data set is the ages of 8 participants.
Age
37
19
31
29
21
26
33
36
First, order the values from low to high to identify the lowest value (L) and the highest value (H).

Age
19
21
26
29
31
33
36
37
Then subtract the lowest from the highest value.

R = H – L

R = 37 – 19 = 18

The range of our data set is 18 years.

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🚨Break Even Point

⚠️is the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business. In other words, you've reached the level of production at which the costs of production equals the revenues for a product.

💡How to calculate your break-even point
When determining a break-even point based on sales dollars: Divide the fixed costs by the contribution margin. ...
Break-Even Point (sales dollars) = Fixed Costs ÷ Contribution Margin.
Contribution Margin = Price of Product – Variable Costs.

🚨🚨

🚨Deflation

🔺
reduction of the general level of prices in an economy.
"a time of high unemployment and deflation"

🚨Inflation

🔺
a general increase in prices and fall in the purchasing value of money.
"policies aimed at controlling inflation"

🚨How to calculate inflation rate
🔺
New amount-Old amount÷Old amount × 100

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Did you know?

How to calculate VAT is actually easy😉

N.B Vat is 15% in 🇿🇦

•Vat inclusive=Amount×(%given+100)

e.g Calculate Vat inclusive on R500
~R500×(15+100)%
=R500×115%
=R575
Or
~R500×15%
=R500+75
=R575🤲

•Vat exclusive (is only calculated on an inclusive amount)=Amount×100÷115

e.gCalculate vat exclusive on R575
~R575×100÷115
=R500🤲

•Calculating Vat on a Vat exclusive Amount=Amount×15%

e.gCalculate the Vat Amount on R500
~500×15%
=R75 (vat amount)🤲

•Calculating Vat on inclusive amount...

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