Calculate Compound Interest: £600 Loan at 24% Annual Rate for 12 Years

Question

Evie takes out a loan of £600. It gains compound interest at a rate of 24% per year. How much money will Evie owe after 12 years? Give your answers in pounds to the nearest 1p.

Accepted Answer

£6780.57

Answer

Step 1: Recall the compound interest formula: $A = P(1 + r)^t$, where $A$ is the final amount owed, $P$ is the principal (initial loan amount), $r$ is the annual interest rate in decimal form, and $t$ is the time in years. Step 2: Identify the values from the problem: $P = £600$, $r = 24\% = 0.24$, $t = 12$ years. Step 3: Substitute the values into the formula: $A = 600(1 + 0.24)^{12}$. Step 4: Calculate $1.24^{12}$ first. Using a calculator, $1.24^{12} \approx 11.30095$. Step 5: Multiply the result by the principal: $A = 600 \times 11.30095 \approx 6780.57$. Step 6: Round the result to the nearest 1p, which gives £6780.57.