JSS 3 Mathematics Second Term Week 3
Topic: COMPOUND INTEREST
Simple Interest
Interest is the payment given for saving money. It can also be the price paid for borrowing money. When interest is calculated on the basic sum of money saved (or borrowed) it called simple interest.
To find the simple interest, use this formula: Interest = Principal × Rate of interest × Time
The principal is the amount of money you borrow or invest.
The rate of interest is the percent charged for the use of money, the percentage charged will be divided by hundred to get the actual value for application in solving a problem.
Exercises
Compute the interest if the principal is 2000 dollars at a rate of interest of 5% for 4 years.
Using a calculator,
Interest = 2000 × 5% × 4 = 2000 × 0.05 × 4
Interest = 100 × 4 = 400
Exercises
Compute the interest if the principal is 2,000,000 dollars at a rate of interest of 4% for a year
Using a calculator,
Interest = 2,000,000 × 4% × 1
Interest = 2,000,000 × 0.04 × 1
Interest = 80,000 × 1 = 80,000
If you have 2 million dollars and your bank pay you 4% interest every year, you will earn 80,000 dollars every year.
Great, you can quit your day time job!
Exercises
Compute the interest if the principal is 100 dollars at a rate of interest of 2% for 10 year
Using a calculator,
Interest = 100 × 2% × 10
Interest = 100 × 0.02 × 10
Interest = 2 × 10 = 20
With little money invested and low interest, 10 years investment gives you a mere 20 dollars
This might be a waste of time!
Compound Interest
When money is saved with simple interest, the interest is paid at regular intervals and the principal remains the same.
With compound interest the interest is added to the principal at the end of each interval.
Thus, the principal increases and so the interest becomes greater for each interval. Most savings schemes give compound interest, not simple interest.
Example
Find the compound interest on N60 000 for 2 years at 8% per annum.
Note: ‘per annum’ means ‘each year’.
The interest is added at 1 year intervals.
1st year: I1 = N 60 000 X 8 X 1/100 = N 4 800
Amount at end of 1st year = N60 000 + N4 800 = N64 800
2nd year: The principal is now N64 800
= N648 X 8 = N5 148
Amount at end of 2nd year = N64 800 + N5 184
= N69 984
Compound interest = N69 984 – N60 000 = N9 984
The working is easier if arranged in a table. The annual interest can be calculated by inspection. For example, 6% of N21 000 is found by multiplying N21 000 by 6, and moving the digits two places to the right (to divide by 100:; i.e.
6% of N21 000 = N210 X 6 = N1 260
The example below shows how to arrange the working
Example
Find the amount that N5 000 becomes if saved for 3 years at 6% per annum compound interest.
1st year: Principal N5 000
6% Interest + 300 (6/100 X 5 000)
—————-
2nd year: Principal N5 300
6% Interest + 318 (6/100 X 5 300)
—————-
3rd year: Principal 5 618
6% Interest + 337.08 (6/100 X 5 618)
——————
Amount N 5 955.08
Exercise
Find the a. amount b. the compound interest, for each of the following
1. N40 000 for 2 years at 8% per annum
2. N60 00 for 2 years at 7% per annum
3. N50 000 for 2 years at 6% per annum
When calculating compound interest, the arithmetic often gives final answers to many decimal places. Final answers should be rounded to the nearest naira. Such rounding should be left to the last line of the working. If possible, use a calculator to calculate interest.
When money is borrowed, interest must be paid back as well as the principal. When a large sum of money is paid back over a number of years, the principal gradually reduces.
Depreciation
Many items, such as cars, clothes, electrical goods, lose values and time passes. This loss in value is called depreciation. Depreciation is usually given as a percentage of the item’s value at the beginning of the year. For example, if a radio costing N10 000 depreciates by 20% per annum, then its value will be N8 000 at the end of the first year. At the end of the second year, its value will be N8 000 less 20% of N8 000, i.e. N8 000 – N1 6000 = N 6 400.
Example
A car costing N680 000 depreciates by 25% in its first year and 20% in its second year, Find its avalue after 2 years.
1st year:
Value of car N680 000
25% depreciation – 170 000 (1/4 of 680 000)
——————–
2nd year:
Value of car 510 000
20% depreciation – 102 000 (1/5 of 510 000)
Value after 2 yr = N408 000
Inflation
Due to rising prices, money loses its value as time passes. Loss in value of money is called inflation. Inflation is usually given as the percentage increase in the cost of buying things from one year to the next. For example, if the rate of inflation 15% per annum, then a CD player which cost N10 000 a year ago will now cost N11 500. Money has lost it’s a value since it now costs more to buy the same thing.
Example
How long will it take for prices to double if the rate of inflation is 20% per annum?
Start with an initial cost of 100 units.
Initially, cost = 100
rise = 20
—————-
after 1 year, cost = 120
rise = 24 (i.e. 20% of 120)
—————
after 2 years, cost = 144
rise = 28.8 (20% of 144)
—————-
after 3 years, cost = 172.8
rise = 34.56 (20% of 172.8)
The cost after 4 years is a little more than double the initial cost. Hence prices will double in just under 4 years.