Find the amount of money that Ruby will have in the bank after 3 years.

Show that Ying will have 7545 USD in the bank at the end of 10 years.

Find the number of complete years it will take for Ying’s investment to first exceed 6500 USD.

Find the number of complete years it will take for Ying’s investment to exceed Ruby’s investment.

Ruby moves from the USA to Italy. She transfers 6610 USD into an Italian bank which has an exchange rate of 1 USD = 0.735 Euros. The bank charges 1.8 % commission.

Calculate the amount of money Ruby will invest in the Italian bank after commission.

Ruby returns to the USA for a short holiday. She converts 800 Euros at a bank in Chicago and receives 1006.20 USD. The bank advertises an exchange rate of 1 Euro = 1.29 USD.

Calculate the percentage commission Ruby is charged by the bank.

5000 + 3 × 230 = 5690     (M1)(A1)(G2)

Note: Accept alternative method.

[2 marks]

\({\text{A}} = 5000{\left( {1 + \frac{{4.2}}{{100}}} \right)^{10}}\) or equivalent     (M1)(A1)

\( = 7544.79 \ldots \)     (A1)

\( = 7545{\text{ USD}}\)     (AG)

Note: Award (M1) for correct substituted compound interest formula, (A1) for correct substitutions, (A1) for unrounded answer seen.

If final line not seen award at most (M1)(A1)(A0).

[3 marks]

5000(1.042)ⁿ > 6500     (M1)(A1)

Notes: Award (M1) for setting up correct equation/inequality, (A1) for correct values.

Follow through from their formula in part (b).

OR

List of values seen with at least 2 terms     (M1)

Lists of values including at least the terms with n = 6 and n = 7     (A1)

Note: Follow through from their formula in part (b).

OR

Sketch showing 2 graphs, one exponential, the other a horizontal line     (M1)

Point of intersection identified or vertical line     (M1)

Note: Follow through from their formula in part (b).

n = 7     (A1)(ft)(G2)

[3 marks]

5000(1.042)ⁿ > 5000 + 230n     (M1)(A1)

Note: Award (M1) for setting up correct equation/inequality, (A1) for correct values.

OR

2 lists of values seen (at least 2 terms per list)     (M1)

Lists of values including at least the terms with n = 5 and n = 6     (A1)

Note: One of the lists may be written under (c).

OR

Sketch showing 2 graphs of correct shape     (M1)

Point of intersection identified or vertical line     (M1)

n = 6     (A1)(ft)(G2)

Note: Follow through from their formulae used in parts (a) and (b).

[3 marks]

6610 × 0.735     (M1)

= 4858.35     (A1)

4858.35 × 0.982(= 4770.8997...)     (M1)

= 4771 Euros     (A1)(ft)(G3)

Note: Accept alternative method.

[4 marks]

800 × 1.29 (= 1032 USD)     (M1)(A1)

Note: Award (M1) for multiplying by 1.29, (A1) for 1032. Award (G2) for 1032 if product not seen.

(1032 – 1006.20 = 25.8)

\(25.8 \times \frac{100}{1032} \%\)     (A1)(M1)

Note: Award (A1) for 25.8 seen, (M1) for multiplying by \(\frac{100}{1032}\).

OR

\(\frac{1006.20}{1032} = 0.975\)     (M1)(A1)

OR

\(\frac{1006.20}{1032} \times 100 = 97.5\)     (M1)(A1)

\( = 2.5{\text{ }}\% \)     (A1)(G3)

Notes: If working not shown award (G3) for 2.5.

Accept alternative method.

[5 marks]

Most of the students read carefully the instruction written in the heading of the question and therefore gave their answers with the accuracy stated but some did not.

Simple interest was well done as well as compound interest with only a small minority of candidates making no progress. A number of students lost the answer mark in (b) for not showing the unrounded answer before writing the answer given. It is also important to mention that calculator commands are not accepted as correct working and therefore full marks are not awarded. Also, some candidates wrote their answers without showing any working leading to a number of marks being lost.

Most of the students read carefully the instruction written in the heading of the question and therefore gave their answers with the accuracy stated but some did not.

Simple interest was well done as well as compound interest with only a small minority of candidates making no progress. A number of students lost the answer mark in (b) for not showing the unrounded answer before writing the answer given. It is also important to mention that calculator commands are not accepted as correct working and therefore full marks are not awarded. Also, some candidates wrote their answers without showing any working leading to a number of marks being lost.

Most of the students read carefully the instruction written in the heading of the question and therefore gave their answers with the accuracy stated but some did not.

Simple interest was well done as well as compound interest with only a small minority of candidates making no progress. A number of students lost the answer mark in (b) for not showing the unrounded answer before writing the answer given. It is also important to mention that calculator commands are not accepted as correct working and therefore full marks are not awarded. Also, some candidates wrote their answers without showing any working leading to a number of marks being lost.

Most of the students read carefully the instruction written in the heading of the question and therefore gave their answers with the accuracy stated but some did not.

Simple interest was well done as well as compound interest with only a small minority of candidates making no progress. A number of students lost the answer mark in (b) for not showing the unrounded answer before writing the answer given. It is also important to mention that calculator commands are not accepted as correct working and therefore full marks are not awarded. Also, some candidates wrote their answers without showing any working leading to a number of marks being lost.

It was nice to see many students recovering after part (d) and to gain full marks in the last two parts of the question.

Most of the students read carefully the instruction written in the heading of the question and therefore gave their answers with the accuracy stated but some did not.

Simple interest was well done as well as compound interest with only a small minority of candidates making no progress. A number of students lost the answer mark in (b) for not showing the unrounded answer before writing the answer given. It is also important to mention that calculator commands are not accepted as correct working and therefore full marks are not awarded. Also, some candidates wrote their answers without showing any working leading to a number of marks being lost.

It was nice to see many students recovering after part (d) and to gain full marks in the last two parts of the question.

Most of the students read carefully the instruction written in the heading of the question and therefore gave their answers with the accuracy stated but some did not.

Simple interest was well done as well as compound interest with only a small minority of candidates making no progress. A number of students lost the answer mark in (b) for not showing the unrounded answer before writing the answer given. It is also important to mention that calculator commands are not accepted as correct working and therefore full marks are not awarded. Also, some candidates wrote their answers without showing any working leading to a number of marks being lost.

It was nice to see many students recovering after part (d) and to gain full marks in the last two parts of the question.