Eva invests \({\text{USD}}2000\) at a nominal annual interest rate of \(8\% \) compounded half-yearly.

Calculate the value of her investment after \(5\) years, correct to the nearest dollar.

Toni invests \({\text{USD}}1500\) at an annual interest rate of \(7.8\% \) compounded yearly.

Find the number of complete years it will take for his investment to double in value.

\(2000{(1.04)^{10}}\)     (M1)(A1)

Note: (M1) for substitution into CI formula. (A1) for correct substitution.

\(2960\)     (A1)

Note: Award the final A1 for rounding their answer correctly to the nearest Yuan.

OR

\(2000{\left( {1 + \frac{8}{{200}}} \right)^{10}} - 2000\)     (M1)(A1)

Note: (M1) for substitution into CI formula. (A1) for correct substitution.

\(2960\)     (A1)     (C3)

Note: Award the final A1 for rounding their answer correctly to the nearest Yuan.

\(1500{(1.078)^n} = 3000\)     (M1)(M1)

Note: (M1) for correct substitution in CI formula, (M1) for \(3000\) seen.

\(n = 10{\text{ years}}\)     (\(n = 9.23{\text{ years}}\) not accepted)     (A1)

OR

\(1500{(1.078)^n} - 1500 = 1500\)     (M1)(M1)

Note: (M1) for correct substitution in CI formula, (M1) for \(1500\) seen.

\(n = 10{\text{ years}}\)     (\(n = 9.23{\text{ years}}\) not accepted)     (A1)

OR

(M2) for list or graph.     (M2)

\(n = 10{\text{ years}}\)     (\(n = 9.23{\text{ years}}\) not accepted)     (A1)

Note: If simple interest formula is used in both parts (a) and (b) then award (M0)(M0)(A0) in (a) and

(b) \(1500 = \frac{{1500(7.8)n}}{{100}}\)     (M1)(A1)

(M1) for substitution in SI formula or lists, (A1) for correct substitution.

\(n = 13\)     (A1)     (C3)

Note: Correct answer only. If \(9.23\) seen without working award (A2).

Note: If calculator notation is used in either part with correct unrounded answer award (A1)(d) only if (FP) is applied in (a) or (AP) in (b). Otherwise (A2)(d) if penalty has already been applied in a previous question.

The use of the TVM solver, and consequent lack of working, was a source of concern; candidates are advised still to write down substituted formulas prior to using the TVM solver.

The use of \(8\% \) in the second part was a common error. The compounding period was again a discriminator for the candidature.

The use of the TVM solver, and consequent lack of working, was a source of concern; candidates are advised still to write down substituted formulas prior to using the TVM solver.

The use of \(8\% \) in the second part was a common error. The compounding period was again a discriminator for the candidature.