Find the simple interest on a loan of $\$ 29,500$ at $5.2 \%$ interest for 10 months Give your answer to the nearest cent
Solution
Step 1 ：We are given a loan amount (P) of $29,500, an interest rate (R) of 5.2%, and a time period (T) of 10 months. We are asked to find the simple interest (I) on this loan.
Step 2 ：First, we need to convert the interest rate from a percentage to a decimal. We do this by dividing the percentage by 100. So, \(R = \frac{5.2}{100} = 0.052\).
Step 3 ：Next, we need to convert the time from months to years, since the formula for simple interest uses time in years. We do this by dividing the number of months by 12. So, \(T = \frac{10}{12} = 0.8333333333333334\) years.
Step 4 ：Now we can use the formula for simple interest, which is \(I = PRT\). Substituting the given values, we get \(I = 29500 \times 0.052 \times 0.8333333333333334\).
Step 5 ：Calculating the above expression, we find that \(I = 1278.3333333333335\).
Step 6 ：Rounding to the nearest cent, we get \(I = 1278.33\).
Step 7 ：So, the simple interest on a loan of $29,500 at 5.2% interest for 10 months is approximately \(\boxed{1278.33}\).
