Simple Interest Part One - A Guide to Improving Your Finances

Question

Part 2 Part 3

Interest is a key concept in financial transactions, where one party borrows money from another. The borrower, referred to as person A, is obligated to pay a certain amount of money to the lender, referred to as person B, for the use of the borrowed funds. This additional amount, paid on top of the borrowed money (also known as the principal), is called interest. The total money that A borrows from B is termed the principal, while the total money paid back by A to B, which includes both the principal and the interest, is called the amount.

In simpler terms:
- Amount = Principal + Interest

Interest is typically charged over a specified period, often expressed as a percentage of the principal. This percentage is called the rate of interest, and it can be applied for different periods such as annually, semi-annually, quarterly, or monthly. For example, if the rate of interest is 5% per annum, the interest payable on $500 for one year will be $25.

There are two main types of interest:
1. Simple Interest
2. Compound Interest

In this chapter, we'll focus on simple interest, where the interest is paid only on the principal amount.

I. Simple Interest

Simple interest is calculated on the principal amount for the entire duration the money is borrowed. The formula for simple interest is:

SI=  P&#215;R&#215;T  100

Where:
- P = Principal (the original amount of money borrowed)
- R = Rate of interest (expressed as a percentage per annum)
- T = Time (the duration for which the money is borrowed, usually in years)

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For example, if you borrow $100 at an interest rate of 5% per annum, the interest for one year will be $5. At the end of two years, the total amount payable will be $110 ($100 + $10 interest for two years).

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Example :

Find the simple interest on $5,200 for 2 years at a rate of 6% per annum.

- Principal P = 5,200
- Time T = 2 years
- Rate R = 6%

Using the formula:

SI=  P&#215;R&#215;T  100  =  5,200&#215;6&#215;2  100  =624

Thus, the simple interest is $624.

II. Basic Formulas for Simple Interest

Here are some additional key formulas related to simple interest:

A. Formula For Principal

The formula to find the principal if you know the simple interest, rate, and time is:

P=  SI&#215;100  R&#215;T

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Example:

A person earns $450 as interest in 2 years on a sum invested at 12% per annum. Find the sum invested.

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- Interest SI = 450
- Time T = 2 years
- Rate R = 12%

Using the formula:

P=  450&#215;100  12&#215;2  =1,875

Thus, the sum invested was $1,875.

B. Formula For Rate of Interest

The formula to find the rate of interest if you know the simple interest, principal, and time is:

R=  SI&#215;100  P&#215;T

Example:

At what rate per annum will a sum of $5,000 amount to $6,000 in 4 years?

- Principal P = 5,000
- Amount A = 6,000
- Time T = 4\) years

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First, calculate the interest:

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SI = A - P = 6,000 - 5,000 = 1,000

Now, use the formula to find the rate:

R=  1,000&#215;100  5,000&#215;4  =5%

Thus, the rate of interest is 5% per annum.

C. Formula For Time

The formula to find the time if you know the simple interest, principal, and rate is:

T=  SI&#215;100  P&#215;R

Example:

In how many years will $1,200 earn an interest of $240 at 5% per annum?

- Principal P = 1,200
- Interest SI = 240
- Rate R = 5%

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Using the formula:

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T=  240&#215;100  1,200&#215;5  =4&#160;years

Thus, it will take 4 years to earn $240 as interest.

D. Formula For Amount

The total amount payable at the end of the loan period is the sum of the principal and the simple interest:

A = P + SI

Alternatively, you can use the following formula to find the amount directly:

A=P&#215;  1+  R&#215;T  100

Example:

Gabriel borrowed $3,000 from Daniel at 15% per annum for 3 years. Find the interest and the total amount returned by Gabriel.

- Principal P = 3,000
- Rate R = 15%
- Time T = 3 years

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First, calculate the interest:

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SI=  3,000&#215;15&#215;3  100  =1,350

Now, calculate the amount:

A = P + SI = 3,000 + 1,350 = 4,350

Thus, Gabriel will return a total amount of $4,350.

Exercise

Now that you have a thorough understanding of simple interest, try these exercises to test your knowledge:

Find the simple interest on $8,000 for 5 years at 7% per annum.
	If a sum of money triples itself in 10 years, find the rate of interest per annum.
	John invests $4,500 at 6% per annum. How long will it take for him to earn $1,620 in interest?
	At what rate per annum will a sum of $2,000 amount to $2,600 in 3 years?
	Mary earns $750 as interest in 5 years on a sum invested at 8% per annum. Find the sum she invested.

Part 2

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