Simple Interest

Simple Interest

Calculating Simple Interest (S.I.)

Why interest?

• Sometimes we need to borrow things.

• It could be as small as a pen, a pencil or a ruler.

• You may need to borrow a phone to make a call or money to buy a snack.

• We can return the pen, the pencil, the ruler or the money borrowed to buy the snack or make the call very easily.

• Sometimes, however, you may need to borrow money on a larger scale from the bank or credit union, for example.

The cost of borrowing money

• Borrowing money from a financial institution comes at a cost.

• The cost of borrowing money is called interest.

• Interest is defined as money paid regularly at a particular rate for the use of money lent, or for delaying the repayment of a debt.

• Interest can be calculated in two ways: simple interest and compound interest.

Simple vs. Compound Interest

• Simple interest is calculated on the principal or original amount of a loan.

• Compound interest is calculated on the the principal amount and also on the accumulated interest of previous periods (interest on interest).

• It is better to borrow with a simple interest loan.

• Compound interest is best for investment (it is better to save or invest on a compound interest plan).

Terms used

• The sum of money you wish to borrow is the Principal (P).

• The agreed percentage of the amount borrowed or invested is the Rate (R).

• The time taken to repay the loan or to invest is the time (T).

• The Simple Interest (S.I.) is the percentage of the principal that accumulates over time.

Calculating Simple Interest (S.I.)

• Simple interest is calculated using the following formula:

•  $S.I.\ =\ \frac{PRT}{100}$  

• Note:- We can find any quantity represented in the formula once we have all other quantities.

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Example 1

Find the interest paid on $2500 if it is borrowed at 25% per annum for 2 years.

Solution

P = $2500
R = 25%
T = 2 years

 $S.I.\ =\ \frac{PRT}{100}=\frac{2500\ \times25\times2}{100}=\text{}1250$  

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Example 2

Find the interest on $3000 if it is borrowed at 6% for 3 years.

Solution

P = $3000
R = 6%
T = 3 years

 $S.I.\ =\ \frac{PRT}{100}=\frac{3000\times6\times3}{100}=\text{540}$  

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Example 3

Find the interest on $5000 if it is borrowed at 5% for 6 months.

Solution

P = $5000
R = 5%
T = 6 months = 0.5 year

 $S.I.\ =\ \frac{PRT}{100}=\frac{5000\times5\times0.5}{100}=125$  

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Example 4

Find the amount to be repaid on a loan of $37000 if it is borrowed at a rate of

 $3\ \frac{1}{3}$  % for 18 months.

Solution

P = $37000
R =  $3\ \frac{1}{3}\%=\frac{10}{3}\%$  

T = 18 months =  $\frac{3}{2}$  years
 $S.I.\ =\ \frac{PRT}{100}=\frac{37000\times\frac{10}{3}\times\frac{3}{2}}{100}=1850$  


Amount to be repaid = $37000 + $1850 = $38850

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Example 5

(a) Calculate the simple interest collected by a bank if $1500 is loaned for 3 years at 8% per annum.

(b) What amount of money did the borrower pay the bank?

(c) What amount was paid monthly?

[input your answers as $a, $b, $c]

Solution

(a) P = $1500 ; R = 8% ; T = 3 years

 $S.I.=\frac{PRT}{100}=\frac{1500\times8\times3}{100}=360$  

(b) Amount repaid = $1500 + $360 = $1860

(c) Amount paid monthly =  $1860\div36=51.67$  

Note: 3 years = 3 x 12 = 36 months

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Example 6

Mr. Isaacs borrowed $3680 from a bank for 6 months at 8.75% per annum. Calculate

(a) the sum of money Mr. Isaacs had to pay the bank as simple interest

(b) the total amount of money repaid to the bank

(c) the amount of money paid monthly.

[input your answers as $a, $b, $c]

Solution

(a) P = $3680 ; R = 8.75% ; T = 6 months = 0.5 year

 $S.I.\ =\frac{PRT}{100}=\frac{3680\times8.75\times0.5}{100}=161$  

(b)Total amount repaid = $3680 + $161 = $3841

(c) Amount paid monthly =  $\text{3841}\div6$  = $640.17