Final answer:
Using the simple interest formula, we determined that Benjamin took out a loan at 8% interest rate and after 8 years, he owes a total of £2952, which means 8 years have passed since he took out the loan.
Step-by-step explanation:
To determine how many years have passed since Benjamin took out the loan, we need to use the formula for simple interest, which is I = Prt, where I is the interest, P is the principal amount borrowed, r is the rate of interest per year, and t is the time in years. In this case, Benjamin borrowed £1800 at a simple interest rate of 8% per year, and he now owes a total of £2952. We first calculate the total interest paid by subtracting the principal from the total amount owed: £2952 - £1800 = £1152 in interest.
We then rearrange the simple interest formula to solve for t:
t = I / (Pr). This gives us t = £1152 / (£1800 * 0.08). After calculating this, we find that t = 8 years, which means 8 years have passed since he took out the loan.