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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

originally

### 3 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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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

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (9 lesson ratings) (9)
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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
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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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