Simple Interest

 

Interest is the extra money gained on an investment or the extra money owed on a loan. The basic way used to find the amount of interest on an investment or a loan is the simple interest formula:

I = Prt

where I = interest, P = principal (the initial amount invested or borrowed), r = the rate of interest, and t = the amount of time (or the term) of the loan or investment. The rate of interest and the amount of time must have matching units. Usually an annual rate is given, thus the time must be in years.

 

·        If one borrows $2000 for 3 years at a 13% annual simple interest rate, what is the interest?

I = Prt

I = ($2000)(.13)(3)

I = $780

             

The interest is $780.  For the loan, one would pay the $2000 borrowed plus an additional $780 for a total amount owed of $2780.

 

·        What is the interest gained with a $1500 simple interest investment at 8% annual rate for 9 months?

 

Notice that the time is given in months, and since we have an annual interest rate, we must convert the time to years.

I = Prt

I = ($1500)(.08)(9¸12)

I = $90

The interest is $90.  For the investment, one would get the $1500 invested plus and additional $90 for a total amount received at the end of 9 months of $1590.

 

In the simple interest formula, you can solve for any of the four quantities if any three of them are known.

 

·        One needs $500 in 2 years.  What annual rate does a simple interest investment need if the initial investment is $200?

 

In this case, we want the interest rate.  We will have $500 in 2 years, but starting with $200.Therefore, the principal is $200, the interest is $500 - $200 = $300.  $300 is the extra money we made on top of the $200 initial amount. Thus:

I = Prt

$300 = ($200) r (2)

r = $300¸($200*2)

r = .75 or 75%

                        The interest rate is 75%

 

·        How much time does it take $3000 to double if the annual simple interest rate is 20%?

 

In this case, we are solving for time.  Since we are doubling $3000 (to $6000), we made an additional $3000 on this investment, which is the interest.  Therefore:

I = Prt

$3000 = $3000 (.20) t

t = $3000¸($3000*.20)

t = 5

                        The amount of time is 5 years.

 

Exercises

  1. What is the interest on a $650 simple interest loan with a 10% rate for 18 months?

 

  1. What is the total amount made on a $1000 simple interest investment if the rate is 8% and the term is 3 years?

 

  1. What is the Principal of a 2-year loan if the interest is $100 with a rate of 6%? (Round answer to whole cents)

 

  1. What is the annual interest rate if an initial investment of $750 becomes $2200 in 8 years? (Round answer to four decimal places)

 

  1. What is the amount of time in years if an initial investment of $2000 becomes $2900 with an annual interest rate of 11%? (Round answer to four decimal places)

 

Solutions:

  1. $97.50
  2. $1240.00
  3. $833.33
  4. .2417 or 24.17%
  5. 4.0909 years

 

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