Money is borrowed at 12% simple interest. After 1 year, 761.60 pays off the loan. How much was originally borrowed

Answer 1

The loan is paid off in (exactly) one year. The simple interest rate is 12%. The payoff amount is $761.60.

Original principal (P) times 12% is the simple interest amount. $761.60 represents the interest plus the amount of the loan. So,

P × I + P = $761.60, where I is the annual simple interest rate.

We can factor P from the expression on the left-hand side of the equation:

P × ( 0.12 + 1 ) = P × 1.12 = 1.12P = $761.60

If we divide both sides by 1.12, we find that

P = $680 exactly.

To check, we just multiply $680 by 12% and then add that to $680.

$680 × 12% = $81.60

And, using our original equation above,

$680 + $81.60 = $761.60

Answer 2

761.60 = A₀(1 + 0.12·1); A₀ = 761.60/1.12 = $679.57