Foundation June 2023 Paper 2 Q23
23. Heath has £3000 to invest for five years.
No extra money will be paid in or withdrawn during these five years.
He is going to choose one of these accounts.
| Account A 4% compound interest per year Interest rates can vary | Account B Guaranteed interest at the end of 5 years of £190 for each £1000 invested |
(a)
Which account gives Heath the greater percentage increase in his money at the end of 5 years and by how much is it greater?
Show how you decide. State any assumption that you make. [6]
Account ………… gives the greater percentage increase by ………… %
Assumption …………………………
(b) Comment on the effect that your assumption in part (a) has had on your decision. [1]
| Scheme | Marks | Comments |
|---|---|---|
| \(3000\times1.04^5\) | M1 | Or equivalent full and complete method |
| = (£)3649.95(87..) or (£)3649.96 or (£)3650 | A1 | |
| \(\dfrac{3649.96-3000}{3000}\,(\times100)\) oe AND \(\dfrac{3\times190}{3000}\,(\times100)\) oe OR \(\dfrac{3649.96-3\times190}{3000}\) (x 100) | M2 | FT ‘their 3649.96’ provided M1 previously awarded M1 for either \(\dfrac{3649.96-3000}{3000}\,(\times100)\) or \(\dfrac{3\times190}{3000}\,(\times100)\) providing M1 previously awarded |
| A indicated AND 2.7(%) or 2.66...(%) | A1 | FT. Allow 2(%) or 2.6(%) or 3(%). |
| Valid assumption e.g. ‘Account A interest rate stays the same’ ‘Account A interest rate does not vary’ ‘Account A interest rate does not go up or down’ | E1 | Do not allow ‘Account A, interest rate can vary’ ‘Account A interest rate is not guaranteed’ |
Alternative
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| \(1.04^5\times100-100\) oe | M2 | \(= 1.2166....\times100-100\) M1 for \(1.04^5\) |
| 21.7(%) or 21.66....(%) | A1 | Allow 21(%) or 21.6(%) or 22(%) |
| (3 × 190) ÷ 3000 (× 100) (=19%) | M1 | FT providing M1 previously awarded |
| A indicated AND 2.7(%) or 2.66...(%) | A1 | FT providing M1 M1 previously awarded Allow 2(%) or 2.6(%) or 3(%) |
| Valid assumption e.g. ‘Account A interest rate stays the same’ ‘Account A interest rate does not vary’ ‘Account A interest rate does not go up or down’ | E1 | Do not allow ‘Account A - interest rate can vary’ ‘Account A interest rate is not guaranteed’ |
Possible misprint (note from Westie's Workshop)
- The second M2 method, \(\dfrac{3649.96-3\times190}{3000}\) (×100), gives 102.67…%, not the 2.67% in the A1 line. Either subtract 100 from it, or the board may have meant \(\dfrac{3649.96-3000-3\times190}{3000}\).
We have left the board's wording exactly as printed. Original: see the board's mark scheme PDF (link above).
| Scheme | Marks | Comments |
|---|---|---|
| Valid impact based on assumption e.g. ‘Even if the interest rate went up, the answer would still be account A but the difference would be more.’ ‘If the interest rate went down, account A may not have the greater increase.’ ‘If the interest rate doesn’t stay the same, then Account A could have even more money than B or less than B’ | E1 | If no valid assumption is made then this mark cannot be awarded. E0E1 not allowed. Allow ‘the answer could be different’. Do not allow ‘the answer could be wrong’. |
| (7) |