most interest, by $\\text{£}0.46$. This supported conclusion earns the final A1."}]}],"generatedAt":"2026-07-19T07:26:20.130Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"e57266fb-1a13-41d5-acf1-c7d25ce02190","revisionId":"2fa8264c-f104-4e8b-a64e-34f3ceab4533","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":2,"sourceTitle":null,"calculatorUse":"calc","parts":[{"id":"15301e86-2538-47b4-b92a-2efe53861386","label":"a","content":"Sarah places £3200 into a savings account that pays 4.5% compound interest per annum. After $n$ years, the balance in the account is £3816.05.\n\nWork out the value of $n$.","markscheme":"- Method of trial and error: $3200 \\times 1.045^3 = 3651.72$ M1\n- Correct value: $3200 \\times 1.045^4 = 3816.05$, so $n = 4$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Evidence of trial and error using the compound interest formula with at least one value for $n$.","code":"M"},{"id":"p2","marks":1,"description":"Identifies $n = 4$ correctly from calculation.","code":"A"}],"finalAnswers":["4"],"generatedAt":"2026-05-06T14:00:50.454Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"trial_and_error","label":"Trial and error","steps":[{"type":"text","order":0,"title":"Find the multiplier","content":"A yearly increase of $4.5\\%$ means multiplying the balance by\n\n$$1+\\frac{4.5}{100}=1.045$$\n\neach year. Because the interest is **compound**, the new balance earns interest in the following year.","highlights":[{"text":"4.5% compound interest per annum","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$n=3$"},{"latex":"$$3200\\times 1.045^3=3651.72$"}]},"order":1,"title":"Try three years","description":"Complete a three-year trial. This calculation earns M1."},{"type":"text","order":2,"title":"Compare the balance","content":"After three years, the balance is $£3651.72$, which is below $£3816.05$. Therefore, try the next whole number of years: $n=4$.","highlights":[{"text":"After $n$ years, the balance in the account is £3816.05.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$3200\\times 1.045^4=3816.05$"},{"latex":"$$\\htmlData{anchor=answer}{\\color{@green}{n=4}}$"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}]},"order":3,"title":"Try four years","description":"This balance matches the stated balance, so n = 4. Writing the answer earns A1."}]}],"generatedAt":"2026-07-19T19:08:30.576Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"ec899242-e3d2-4f9f-8463-9e79b977611e","revisionId":"3ee91a84-aab8-4e31-98f8-83637946bb0b","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":"calc","parts":[{"id":"53ec16af-6b5b-41b9-928e-c868d165ab45","label":"a","content":"Liam invests £3500 in a cash ISA paying 5% compound interest per annum. Chloe invests £3800 in a different account paying 4.2% compound interest per annum.\n\nWork out the difference between the amount of money Liam has after 3 years and the amount of money Chloe has after 3 years.","markscheme":"- Liam: $3500 \\times 1.05^3 = £4051.69$ M1\n- Chloe: $3800 \\times 1.042^3 = £4299.02$ M1\n- Difference: $4299.02 - 4051.69$ M1\n- Final answer: $£247.33$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Calculation of Liam's balance after 3 years.","code":"M"},{"id":"p2","marks":1,"description":"Calculation of Chloe's balance after 3 years.","code":"M"},{"id":"p3","marks":1,"description":"Method to find the difference between the two balances.","code":"M"},{"id":"p4","marks":1,"descr

Compound Interest and Depreciation

Question 30

Compound Interest and Depreciation Questions

Compound Interest and Depreciation

Question 30

Compound Interest and Depreciation Questions