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Find the simple interest rate earned on $8200 for 2 years at 11%

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3 Answers

The formula for simple interest is as follows:     I = Prt   ,     where

     I = interest

     P = Principal (amount borrowed)

     r = interest rate (in decimal form)

     t = time (period of time the amount is borrowed for)

Given:        P = $8200

                 r = 11%/100% = 0.11

                 t = 2 years

                 I = ?

          I = Prt

          I = (8200)·(0.11)·(2) = 1804

Therefore, the interest on borrowing $8200 for 2 years at 11% interest rate is $1804.

If you are looking to find the amount to pay back after 2 years, it is the Principal plus the interest which is.....

          Principal + interest = 8200 + 1804 = 10,004   .... 

   ...so the amount to pay back is $10,004

Interest is usually found using two different methods - either simple interest or compound interest.  Each has a different formula.  The simple interest formula has four different variables represented.  Essentially that means you will need to be given three of the variables in order to solve for the fourth variable.

In this case, you were give the variables for the principal (p) - the amount invested (or borrowed), the interest rate (r) - usually given as a percent that must be transformed to a decimal number, and the length of the loan (t) - which must always be in years, never in months.  (If it is given in months, let's say 9 months, then you would have to enter it into the formula as 9/12 of a year.)

This particular question is worded unusually because normally you would be asked to find the "simple interest" given this information.  If you were asked for the "simple interest rate", you would normally be given the interest earned (I), the principal (p), and the length of the loan (t) and be asked to solve for the interest rate (r).

So ... even though the question has confusing wording, because they gave you p, r, and t, you would solve for I, using the formula for simple interest:  I = p x r x t

As a side note - I remember this formula using the mnemonic:  "I am PReTty" :-)  

 

 

I = p · r · t
"I"  is simple interest ($)
"p"  is principal ($)
"r"  is rate (%)
"t"  is time (months or years)
~~~~~~~~~~~ 
11% = 0.11
I = $8200 · 0.11 · 2 = $1804