To find the annual rate of interest as a percent on the musician's loan for the trumpet, we can use the simple interest formula:
$$\sf\:I = P \cdot r \cdot t \\$$
Where:
- - I is the total interest owed (792 in this case)
- - P is the principal amount (2200 in this case)
- - r is the annual interest rate (what we need to find)
- - t is the length of the loan in years (3 in this case)
We can rearrange the formula to solve for r :
$$\sf\:r = \frac{I}{P \cdot t} \\$$
Substituting the given values:
$$\sf\:r = \frac{792}{2200 \cdot 3} \\$$
Now, we can calculate the value of r :
$$\sf\:r = \frac{792}{6600} \\$$
Simplifying the fraction:
$$\sf\:r = 0.12 \\$$
To express this as a percentage, we multiply by 100:
$$\sf\:r = 0.12 \times 100 \\$$
Therefore, the annual rate of interest on the musician's loan for the trumpet is 12%.
