Each year, the value of a certain rare stamp increases by 5% of its value at the beginning of the year. A collector bought the stamp for $10000 at the beginning of 2005. Find its value at the beginning of 2015 correct to the nearest $100.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

1. Uses r = (1.05 or 105%)⁹, ¹⁰ or ¹¹ (B1) Used to multiply repeatedly or in any GP formula.
2. New value = 10000 × 1.05¹⁰ = ($)16 300 (B1)
3. EITHER: n=1 → S₁ = 5, a = 5 (B1) Uses n=1 to find a
4. n=2 → S₂ = 13 (B1) Correct S_n for any other value of n (e.g. n = 2)
5. a + (a + d) = 13 → d = 3 (M1A1) Correct method leading to d =
6. OR: ½n(2a + (n-1)d) = ½n(3n + 7) (M1) maybe be ignored
7. ∴ dn + 2a - d = 3n + 7 → dn = 3n → d = 3 (*M1A1) Method mark awarded for equating terms in n from correct S_n formula.
8. 2a - (their 3) = 7, a = 5 (DM1A1)