Simple Interest (Rearranging the Formula)

Simple Interest

(Rearranging the Formula)

by Shamar Butcher

​Not all Simple Interest questions require you to calculate the interest...

Sometimes, you may have to find the:

• ​Principal, P

• ​Rate, R

• ​Time, T

​Not all Simple Interest questions require you to calculate the interest...

You must remember the Simple Interest Formula because you would have to rearrange it to find the:

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• Principal, ​P

• ​Rate, R

• ​Time, T

Multiple Choice

What is the Simple Interest Formula?

• $$I\ =\ P\ E\ T$$  

• $$I\ =\ \frac{P\ R}{T}$$  

• $$I\ =\ P\ R\ T$$  

• $$I\ =\ P\ R\ T\ \times100$$

​Make P the subject of the formula, I = P R T

1. ​Remember that groups of letters with no signs in-between means that they are multiplied

2. ​Eliminate R and T from the right side by division 

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​3.​ Cancel letters which are the same above and below

​Make T the subject of the formula, I = P R T

1. ​Remember that groups of letters with no signs in-between means that they are multiplied

2. ​Eliminate P and R from the right side by division 

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​3.​ Cancel letters which are the same above and below

Multiple Choice

The steps taken to rearrange the Simple Interest formula to find P and T are the same.

Making R the subject of the Simple Interest formula​

Follow the same steps as for the other two, however....

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​Remember that the Rate was converted from a % to a decimal in the Simple Interest Formula...we need to convert it back to a % when solving for R

​Make R the subject of the formula, I = P R T

1. ​Eliminate P and R from the right side by division 

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2. Cancel letters which are the same above and below

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​3. R currently is in decimal form and NOT a %...we need to multiply by 100 to change it to a %

​Make R the subject of the formula, I = P R T

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​​You should ALWAYS give your answers for R as a %

Open Ended

In the formula for R, why do we multiply by 100?

​Example 1

​Mrs Thomas took a bank loan for 6 months at 14% simple interest. How much did she borrow if the interest on her loan was $126?

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Multiple Choice

​Mrs Thomas took a bank loan for 6 months at 14% simple interest. How much did she borrow if the interest on her loan was $126? 

What are you required to calculate exactly?

• the Principal, P

• the Time, T

• the Interest, I

• the Rate, R

​Example 1 cont'd

​Mrs Thomas took a bank loan for 6 months at 14% simple interest. How much did she borrow if the interest on her loan was $126?

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​T = 6 months = 1/2 year = 0.5 years

​R = 14% = 0.14

​I = $126

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​We have to find P:

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Mrs Thomas initially borrowed $1,800 from the bank.

​Example 2

Calculate the percentage rate per annum if simple interest of $216 is paid when $1,200 is invested for 4 years.

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Multiple Choice

Calculate the percentage rate per annum if simple interest of $216 is paid when $1,200 is invested for 4 years.

What is the Principal, P?

• $216

• $1,200

• $1,416

​Example 2 cont'd

Calculate the percentage rate per annum if simple interest of $216 is paid when $1,200 is invested for 4 years.

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​I = $216

​P = $1,200

​T = 4 years

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​We have to find R:

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The Rate, R is 4.5% per annum.

​QUESTIONS

Rearrange the Simple Interest formula to find:

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​1) P, given that: I = $180, T = 3 years, R = 12 ½%

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​2) R, given that: I = $675, P = $1250, T = 4 years

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​3) T, given that: I = $364, P = $800, R = 13%

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​4) $10,000 is borrowed at 15% p.a. After what length of time is the amount of simple interest equal to the loan?

​Answers: 1) $480 2) 13.5% p.a. 3) 3.5 years 4) 6 ⅔ years or 6 years, 8 months