The table shows the details of a car loan. Amount borrowed Simple interest rate Length of loan Number of payments \(\$9000\) \(8\%\) per year \(3\) years \(...

Simple interest is charged on the original amount borrowed for every year of the loan, so it grows in equal steps: \(I=P\times r\times t\) with \(r\) written as a decimal.

(a) \(9000\times0.08\times3\) [M1] oe. Take it in stages without a calculator: \(8\%\) of \(9000\) is \(720\), and \(3\times720=2160\). The interest is \(\$2160\) [A1].

(b) The total repaid is the amount borrowed plus the interest: \(9000+2160=\$11\,160\) [B1] ft.

(c) The \(36\) payments share the total repaid equally: \(11\,160\div36\) [M1] ft. Since \(36\times300=10\,800\) and the remaining \(360\) gives \(360\div36=10\), each payment is \(\$310\) [A1]. Note that \(36\) payments over \(3\) years is one payment a month, which is consistent.

(d) \(\frac{\text{interest}}{\text{amount borrowed}}=\frac{2160}{9000}\) [M1] ft. Divide both by \(360\): \(\frac{6}{25}\) [A1] cao. (Step by step: divide by \(10\) to get \(\frac{216}{900}\), then by \(9\) to get \(\frac{24}{100}\), then by \(4\) to get \(\frac{6}{25}\).)

Contrast this with compound interest, where the second year's interest would be charged on \(\$9720\) rather than on \(\$9000\). Simple interest keeps the base fixed, which is why the yearly charge here is \(\$720\) every time.