Indicies - Explanation, Examples and Laws of Indicies

 

Understanding Simple Interest: How Money Grows Over Time.

Money doesn’t stay still - it grows or increases when borrowed, saved, or invested. One of the simplest ways to measure this growth is through Simple Interest.

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What is Interest?

Interest is the extra amount paid for using someone else’s money.
When you borrow, you pay interest.
When you save or invest, you earn interest.

There are two main types of interest:

• Simple Interest (S.I.) — where interest is calculated only on the original amount (principal).

• Compound Interest (C.I.) — where interest is calculated on both the principal and previous interests.

This post focuses on Simple Interest — the foundation for understanding all financial growth.

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The Formula for Simple Interest

$$\text{Simple Interest (S.I.)}=\frac{P\times R\times T}{\mathrm{100}}$$

Where:

• $P$ = Principal (the original amount of money)

• $R$ = Rate of interest per year (in %)

• $T$ = Time (in years)

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Worked Examples

Example 1

Find the simple interest on GHS 5,000 for 2 years at 10% per annum(NB: per annum means per year)

$$S\mathrm{.}I\mathrm{.}=\frac{5000\times 10\times 2}{100}=1000$$

Interest = GHS 1,000

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Example 2

Find the total amount to be paid after 3 years if GHS 2,400 is borrowed at 8% per annum.

$$S.I. = \frac{2400 \times 8 \times 3}{100} = 576$$
$$\text{Total Amount} = 2400 + 576 = GHS 2,976$$

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Example 3

A man deposits GHS 4,000 in a bank at 5% per annum. Find his total savings after 4 years.

$$S.I. = \frac{4000 \times 5 \times 4}{100} = 800$$
$$\text{Total}=4000+800=GHS4,800$$

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Example 4

How long will it take GHS 6,000 to earn GHS 900 as simple interest at 5% per annum?

$$900 = \frac{6000 \times 5 \times T}{100}$$ $$900 = 300T$$
$$T = 3 \text{ years}$$

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Example 5

At what rate will GHS 2,000 earn GHS 300 as simple interest in 3 years?

$$300 = \frac{2000 \times R \times 3}{100}$$ $$300 = 60R$$
$$R = 5\%$$

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Example 6

A trader borrows GHS 10,000 for 9 months at 12% per annum. Find the interest.
Since 9 months = $\frac{9}{12} = 0.75$ years,

$$S\mathrm{.}I\mathrm{.}=\frac{10000\times 12\times 0.75}{100}=900$$

Interest = GHS 900

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Example 7

Find the principal that will earn GHS 600 as interest in 4 years at 5% per annum.

$$600 = \frac{P \times 5 \times 4}{100}$$ $$600 = 0.2P$$$$P = 3000$$Interest = GHS 3000

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Example 8

GHS 800 grows to GHS 920 in 3 years. Find the rate of interest.

$$S.I. = 920 - 800 = 120$$$$120 = \frac{800 \times R \times 3}{100}$$ $$120 = 24R$$
$$R=5\mathrm{\%}\mathrm{<br>}$$

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Example 9

Ama invests GHS 2,500 at a certain rate for 2 years and receives GHS 2,900 at the end. Find the rate of interest.

$$S.I. = 2900 - 2500 = 400$$
$$400 = \frac{2500 \times R \times 2}{100}$$ $$400 = 50R$$
$$R=8\mathrm{\%}\mathrm{<br>}$$

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Example 10

A man lent GHS 1,500 to a friend for 5 years. If he received GHS 1,875 at the end, find the rate of interest.

$$S.I. = 1875 - 1500 = 375$$
$$375 = \frac{1500 \times R \times 5}{100}$$ $$375 = 75R$$
$$R = 5\%$$

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Understanding the Total Amount

The Total Amount (A) to be repaid or received is:

$$A = P + S.I.$$

This means that the longer the money stays or the higher the rate, the more the total grows - a principle that applies to savings, loans, and investments alike.

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                     Assignment

Try these to test your understanding :

1. Find the simple interest on GHS 4,500 for 3 years at 6% per annum.

2. What total amount will GHS 1,200 become after 5 years at 10% per annum?

3. Find the rate if GHS 2,000 earns GHS 400 in 4 years.

4. For how long must GHS 3,000 be lent to earn GHS 450 at 5% per annum?

5. Find the principal which amounts to GHS 1,200 in 2 years at 10% per annum.

6. A boy deposits GHS 8,000 in a bank that pays 12% per annum. Find his total balance after 18 months.

7. If the simple interest on a certain sum for 6 years at 4% is GHS 960, find the principal.

8. GHS 5,000 grows to GHS 5,600 in 2 years. Find the rate.

9. A trader borrows GHS 9,000 for 8 months at 10% per annum. Find the interest.

10. A man saves GHS 2,500 in a bank for 4 years. If he receives GHS 3,000 at the end, find the rate of interest.