Question

Tom borrowed $35,000 to remodel his house. At the end of 5-year loan, he had repaid a total of $46,375. At what simple interest rate did he borrow the money? How can I find the answer to this?

Answer 1

The formula for simple interest is I = prt, where I is the amount of interest, p is the principal borrowed, r is the interest rate written as a decimal number, and t is the amount of time in years.  First we find the amount of interest.  He borrowed $35000 but paid back $46375.  That means he paid 46375-35000 = $11375 in interest.  We can now substitute our information into our interest formula:
11375=35000(r)(5)
11375=35000(5)(r) ----- remember that multiplication is commutative
11375=175000r
Divide both sides by 175000 to cancel it:
11375/175000 = 175000r/175000
0.065 = r
To convert this to a percentage, we multiply by 100:
0.065(100) = 6.5%