Questions: You borrow 690 from your brother and agree to pay back 760 in 16 months. What simple interest rate will you pay? % (round to the nearest tenth of a percent)

Solution Steps

To find the simple interest rate, we can use the formula for simple interest:

\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]

First, calculate the interest paid, which is the difference between the amount paid back and the amount borrowed. Then, rearrange the formula to solve for the rate. The time should be in years, so convert 16 months to years. Finally, calculate the rate and convert it to a percentage.

The interest paid is the difference between the amount paid back and the principal borrowed.

\[ \text{Interest} = 760 - 690 = 70 \]

The time given is 16 months. To convert this to years, divide by 12.

\[ \text{Time in years} = \frac{16}{12} = \frac{4}{3} \approx 1.3333 \]

Using the simple interest formula \( \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \), solve for the rate:

\[ \text{Rate} = \frac{\text{Interest}}{\text{Principal} \times \text{Time}} = \frac{70}{690 \times \frac{4}{3}} \approx 0.07609 \]

Convert the rate to a percentage by multiplying by 100 and round to the nearest tenth of a percent.

\[ \text{Rate percentage} = 0.07609 \times 100 \approx 7.6\% \]

Final Answer