Year 11 Maths - General Number Patterns and Recursion

Using Recurrence Relations To Model Growth and Decay

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Questions

Question 1

30662

The following recurrence relation can be used to model a simple interest investment of $2400 paying interest at a rate of 4% per annum. ${v_0} = 2400,\,\,{v_{n + 1}} = {v_n} + 96$. Find the value of the investment after 4 years.

Answer

$\$ 2784$

Worked Solution

\begin{aligned}
v_{0}&=2400 \\
v_{1}&=2400+96\\
v_{2}&=2400+2 \times 96 \\
v_{3} &=2400+3 \times 96 \\
v_{4} &=2400+4 \times 96 \\
&=\$ 2784\\
\end{aligned}

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