Numeracy Higher June 2018 Unit 2 Q9
9.
(a) Circle either TRUE or FALSE for each statement given below. [2]
| STATEMENT | ||
|---|---|---|
| A nominal annual interest rate is not the same as an AER. | TRUE | FALSE |
| A savings account offers a nominal annual interest rate of 2%, with interest paid monthly. After a year, any investment will have increased in value by exactly 2%. | TRUE | FALSE |
| A savings account offers an AER of 2·4%, with interest paid monthly. The monthly interest rate the account offers will be exactly 0·2%. | TRUE | FALSE |
| £100 is invested in a savings account that pays monthly interest at a rate of 1%. There are no further transactions into or out of the account. The amount in the account after a year will be £112. | TRUE | FALSE |
(b) Benjamin invests £1000 into an account that pays interest every 6 months.
He does not make any further payments into the account, and does not withdraw any money either.
After a year, there is £1036 in the account.
He does not make any further payments into the account, and does not withdraw any money either.
After a year, there is £1036 in the account.
Calculate how much was in the account after 6 months.
Give your answer correct to the nearest penny.
You must show all your working. [4]
From the formula list: Annual Equivalent Rate (AER): AER, as a decimal, is calculated using the formula \(\left(1+\dfrac{i}{n}\right)^{n}-1\), where \(i\) is the nominal interest rate per annum as a decimal and \(n\) is the number of compounding periods per annum.
| Scheme | Marks | Comments |
|---|---|---|
| True False False False | B2 | B1 for any 3 correct |
| Scheme | Marks | Comments |
|---|---|---|
| (Amount =) \(\sqrt{\dfrac{1036}{1000}}\) × 1000 or 1·017(84…) × 1000 | M3 | Could be seen in stages M2 for \(\sqrt{\dfrac{1036}{1000}}\) M1 for 1000 × multiplier2 = 1036 or M1 for (1 + i/2)2 – 1 = 0·036 |
| (Amount after 6 months =) (£) 1017.84 | A1 | An unsupported £1018 is awarded M0A0 Note: A final answer of (£) 1017.85 can be awarded M3A0 provided no incorrect work seen |