Final answer:
Brian initially invested $3750 to earn $600 in interest over 10 years at an annual rate of 0.08. Using the formula for simple interest, the principal amount is calculated and matches option C.
Step-by-step explanation:
The question involves simple interest calculation, which is used to determine the initial principal amount invested by Brian. The formula for simple interest is I = PRT, where I is the interest earned, P is the principal amount (initial investment), R is the rate of interest per year, and T is the time in years the money is invested.
Given that Brian earned $600 in interest over 10 years at a rate of 0.08, we can rearrange this formula to solve for P (the initial investment):
P = I / (RT)
Substituting the given values, we get:
P = $600 / (0.08 × 10)
P = $600 / 0.8
P = $750
This result is reached because the interest of $600 generated over 10 years at a rate of 0.08 implies an initial investment of $75 per year (I/T), and dividing this annual investment ($75) by the rate (0.08) gives the original principal amount of $3750.