SIMPLE INTEREST

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Interest is a fee paid for use of someone’s money. Banks, savings and loan companies pay interest periodically for using money deposited in a savings account. When we borrow money, we are expected to pay for using it. This is called interest.

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

There are three components to calculate the simple interest:

 

  • PRINCIPAL (P): This is the amount deposited in the bank or the amount

RATE (R): This is the percentage of interest charged.

  • TIME (T): This is the duration or period of the interest charged or to pay back amount It should always be in years. When not given in years, it should be converted to years before being used to solve.
  • AMOUNT: This is the sum of the principal and the interest given. Put simply, The total money paid back after the given time is called the amount.

Extra money paid back is called the simple interest (S.I). Interest is expressed as rate par cent per annum (p.a.) i.e., 12% per month means, the interest on $100 for 1 year is $12.

Formula for calculating simple interest is S.I = (P × R × T)/100

Important: Formula for calculating amount is A = P + I

Examples

Find simple interest on $2000 at 5% per annum for 3 years. Also, find the amount.

Solution: 

Principal = $2000

Rate = 5% p.a.

T = 3 years

S.I = (P × R × T)/100

= (2000 × 5 × 3)/100

= $ 300

Amount = P + I

= $ ( 2000 + 300 )

= $ 2300

Calculate the simple interest on $ 6400 at 10% p.a. for 9 months.

Solution: 

P = $ 6400

R = 10% p.a.

T = 9 months or 9/12 years

[12 months = 1 year

1 months = 1/12 years

9 months = (1 × 9)/12 years]

Therefore, S.I. = (P × R × T)/100

= (6400 × 10 × 9)/(100 × 12)
= $480

Mike took a loan of $20000 from a bank on 4 February 2009 at the rate of 8% p.a. and paid back the same on 6th July 2009. Find the total amount paid by Mike.

P = $20000

R = 8 % p.a.

T = 152/365

Solution:

Time = February + March +April + May + Jun + July

= 24 days + 31 days + 30 days + 31 days + 30 days + 6 days

= 152 days

Therefore, S.I. = (P × R × T)/100

= (20000 × 8 × 152)/(100 × 365)

= $ (40 × 8 × 152)/73

= $ 666.30

Therefore, the amount paid = $ (20,000 + 666.30) = $ 20666.30

Calculating Rate
At what per cent will $ 1500 amount to $ 2400 in 4 years?

Solution:

P = $ 1500

R = ?

T= 4 years and

A = $ 2400

S.I. = A – P

= $(2400 – 1500 )

= $ 900

S.I. = (P × R × T)/100

900 = (1500 × R × 4)/100

Therefore, R = (900 × 100)/(4 × 1500) = 15%

At what rate percent per annum simple interest will a sum of money double itself in 6 years?

Solution:

Let P = x, then A = 2x

Also, S.I = A – P

= 2x – x

= x

T = 6 years

We know that S.I. = (P × R × T)/100

(x × R × 6)/100 = x

R = 100x/6x = 16.6 %

 

Calculating Time
In how much time will a sum of money triple itself at 15 % p.a.?

Solution:

Let P = x, then A = 3x

So, I = A – P

= 3x – x = 2x

We know that S.I = (P × R × T)/100
2x = (x × 15 × T)/100

T = (2x × 100)/(x × 15) = 40/3 = 13.3 years

A some amounted to $ 2520 at 10% p.a. for the period of 4 years. Find them sum.

Solution:

Let A = $ 2520

R = 10% p.a.

T = 4 years

P = ?

Let the principal be x

S.I = (x × 10 × 4)/100 = 2x/5

A = P + I

A = x + 2x/5

A = (5x + 2x)/5 = 7x/5 [But given that A = $2520]

7x/5 = 2520

7x = 2520 × 5

x = (2520 × 5)/7 = $ 1800

Ron borrowed $ 24000 from his friend at the rate of 12% per annum for 3 years. At the end of the period, he cleared the account by paying $ 10640 cash and giving the cow. Find the price of the cow.
Solution:
Here, P = $24000
R = 12% p.a.
T = 3 years
S.I. = (P × R × T)/100
= (24000 × 12 × 3)/100 = $ 86
Amount = $24000 + 8640 = $ 32640
Now, $10640 + Price of cow = $ 32460
Therefore, price of the cow = $ 32460 – 10640 = $ 22000

Quiz

Amos borrowed N24,000 to buy a TV set. The interest rate was 15%.

Find how interest must Amos pay at the end of the year

Find the total Amos will pay back.

Mrs. Andy borrowed N350,000 to buy shares. At the rate of 15%, how much interest will she pay if she borrowed this amount for 5 years?

Gabriel puts N5000 in a bank which pays interest rate at 7%. How long will it take to gain N350?

Mary put some money in a company that paid 20% simple interest per year. If the interest after 3 years is N15, 000, how much did he invest?

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