Achievement Standard 1.7 Solve straightforward number problems in context.

 The given information is correctly inserted into the formula, it is clear that finding r is the purpose of the calculations.
The value for r is worked out.
  • One algebraic error may be overlooked.
  • The occasional small numerical error may be overlooked.
  • If a small error is consistently used in each of the three calculations, e.g. the year is always out by one, this can be overlooked.
/ (a) / Painting AP = $2880
A = $6500
n = 8yrs (2001 – 1993)
r = ? / A = / P /  Each of the three calculations are clearly attributed to either painting A, B or C.
 The workings for each set of calculations are, for the most part, easy to follow.
 The answer in each instance is underlined or made obvious in some way.
 There should be no rounding used in the process of the calculations though rounding of 4dp is acceptable.
 The prices of the paintings apparently vary from 2 to 4 sf, so the interest rates should be given to a similar level of accuracy, that is anywhere from 2sf to 4sf.
$6500 = / $2800
2.2569 = /
= / 1 + / = 1.1071
0.1071 = / / r = 10.71%
Painting B
P = $1775
A = $9200
n = 5yrs
r = ? / $9200 = / $1775
5.1831 = /
= / 1 + / = 1.3897
0.3897 = / / r = 38.97%
Painting C
P = $3300
A = $18750
n = 12yrs
r = ? / $18750 = / $3300
5.682 = /
= / 1 + / = 1.1558
0.1558 = / / r = 15.58%
 The compound interest formula (or another method) is correctly used to find the relevant information.
NB the figures used must be consistent with the answers gained in (a). / (b) / The compound interest formula is used to calculate “A” the accumulated amount.
The principal is then taken away from this figure to find “I” the interest (or return on the investment) that has been made from the beginning of ‘02. /  The information is presented clearly and logically. (This may not be in a table, but it must be presented sequentially and clearly labelled.)
 The purpose of these calculations is merely to compare the options, not to get precise figures, therefore rounding numbers even to two significant figures is adequate. (Though no rounding should be done in the process of the calculations.)
Year / End of ’02
n = 1 / ’03
n = 2 / ’04
n = 3
Painting A
P = $6500
r = 10.71% / A = $7196
I = $696 / A = $7967
I = $1467 / A = $8820
I = $2320
Painting B
P = $9200
r = 38.97% / A = $12785
I = $3585 / A = $17768
I = $8568
Combination
A + B / I = $4809 / I = $10035
Painting C
P = $18750
r = 15.58% / A = $21671
I = $2921 / A = $250478
I = $6298 / A = $28950
I = $10200
Option one would be the first to return $10000 on the investment, this would occur towards the end of the second year, i.e. 2003. /  There is a clear sentence answer that correctly uses the calculations to come to a conclusion consistent with the figures used.