Hollie takes out a loan of \( £ 800 \). It gains compound interest at a rate of \( 26 \% \) per year. How much money will Hollie owe after 13 years? Give your answer in pounds \( (£) \) to the nearest 1 p.

To find out how much Hollie will owe after 13 years with a loan of £800 at a compound interest rate of 26% per year, we can use the compound interest formula: \[ A = P(1 + r)^n \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial loan amount). - \( r \) is the annual interest rate (in decimal). - \( n \) is the number of years. Plugging in the values: - \( P = 800 \) - \( r = 0.26 \) - \( n = 13 \) This gives us: \[ A = 800(1 + 0.26)^{13} \] \[ A = 800(1.26)^{13} \] Calculating \( (1.26)^{13} \): \[ (1.26)^{13} \approx 14.953 \] Now multiply by the principal: \[ A \approx 800 \times 14.953 \] \[ A \approx 11962.4 \] Therefore, rounding to the nearest penny, Hollie will owe approximately **£11962.40** after 13 years.