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Me. Peterson wrote a check of 7820 to pay off a loan, which was given to him at a rate of 5 percent simple interest for 3 years. How much money did he borrow or

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3 Answers

 In a Simple  interest rate, where Money grows at fixed rate each year is given a linear equation, because rate of change is fixed ( throughout the year). A is the balance of the account after n( variable) years with a fixed rate( slope).
 
 
 
  A = P + Pnr     / here the n is the variable. 
 
 7800 = P( 1 +3(0.05)= 
 
 
     7800 =  P + P( 0.15)
 
    P = 7800 = 6783
           1.15
 
 
 
 
 
i=p*r*t
A=p+i
A=p+p*5%*3
$7820=p+p*0.05*3
$7820=p+p*0.15
$7820=(1+0.15)*p
$7820=1.15*p
$7820/1.15=p
$6800=p, the principal or how much was borrowed
check: i=$6800*0.05*3
           i=$6800*0.15
           i=$1020
A=$6800+$1020=$7820
Hi Noah;
By definition, SIMPLE INTEREST means that there is no compounded interest.
I am assuming that the 5% rate is per year.
$7820=(principal)+[(principal)(rate)(time)]
$7820=(principal)+[(principal)(rate)(time)]
$7820=(principal)+[(principal)(0.05/year)(3 years)]
The unit of year is in the numerator and denominator.  It cancels.
$7820=(principal)+[(principal)(0.05/year)(3 years)]
$7820=(principal)+[(0.15)(principal)]
$7820=(1.15)(principal)
Let's divide both sides by 1.15...
$6800=principal