Maths Maestri Grade 12

Finance, Growth and Decay

Question 7 practice quiz: effective interest, future value annuities, pension withdrawals, and decision-making from a memo-style solution.

Start The 15 Mark Quiz

This quiz follows the supplied memo closely. Each question is worth 1 mark, so your score shows which memo steps are secure.

Grade12 Mathematics
TopicFinance, Growth and Decay
Total15 marks
You are in guest mode. You can practise now, but email results are hidden until you sign in through Maths Maestri.

What this quiz covers

Grade 12 Finance Growth and Decay - Question 7 draws its questions at random from a bank of 15 questions, with full worked solutions for every one.

Worked examples

A few of the question types, with full solutions, so you know what to expect.

Which formula correctly converts Sarah's nominal rate to an effective annual rate?

  1. \(1+i_{\text{eff}}=\left(1+\frac{0.11}{2}\right)^2\)
  2. \(i_{\text{eff}}=\frac{0.11}{2}\)
  3. \(1+i_{\text{eff}}=\left(1+0.11\right)^2\)
  4. \(1+i_{\text{eff}}=1+0.11\times2\)

Answer: \(1+i_{\text{eff}}=\left(1+\frac{0.11}{2}\right)^2\)

Compounded semi-annually means interest is compounded \(2\) times per year.

Use \(1+i_{\text{eff}}=\left(1+\frac{i}{m}\right)^m\).

What is Sarah's effective annual interest rate to two decimal places?

  1. \(11{,}30\%\)
  2. \(11{,}42\%\)
  3. \(5{,}50\%\)
  4. \(11{,}00\%\)

Answer: \(11{,}30\%\)

\(i_{\text{eff}}=\left(1+\frac{0.11}{2}\right)^2-1\).

\(i_{\text{eff}}=0.113025\ldots=11.3025\ldots\%\).

Whose investment earns the higher rate per annum?

  1. Mary's investment, because \(11{,}42\%>11{,}30\%\).
  2. Sarah's investment, because \(11\%\) is compounded twice.
  3. They are equal after converting Sarah's rate.
  4. Sarah's investment, because \(11{,}30\%>11{,}42\%\).

Answer: Mary's investment, because \(11{,}42\%>11{,}30\%\).

The comparison must use Sarah's effective rate, not only her nominal rate.

\(11{,}42\%\) is greater than \(11{,}30\%\).

How many monthly deposits are made?

  1. \(114\)
  2. \(113\)
  3. \(108\)
  4. \(120\)

Answer: \(114\)

From 1 November 2016 to 1 October 2025 gives \(9\times12=108\) payments.

From 1 November 2025 to 1 April 2026 gives \(6\) more payments.

Which monthly interest rate should be used in the annuity calculation?

  1. \(i=\frac{0.0772}{12}\)
  2. \(i=0.0772\times12\)
  3. \(i=\frac{7.72}{12}\)
  4. \(i=\frac{0.772}{12}\)

Answer: \(i=\frac{0.0772}{12}\)

Convert \(7{,}72\%\) to decimal form: \(0.0772\).

Because interest is compounded monthly, divide the annual nominal rate by \(12\).