4 The value, $\pounds V$, of an initial investment, $\pounds P$, at the end of $n$ years is given by the formula

$$V = P \left( 1 + \frac { r } { 100 } \right) ^ { n }$$

where $r \%$ per year is the fixed interest rate.\\
Mr Brown invests $\pounds 1000$ in Barcelona Bank at a fixed interest rate of $3 \%$ per year.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the value of Mr Brown's investment at the end of 5 years. Give your value to the nearest $\pounds 10$.
\item The value of Mr Brown's investment will first exceed $\pounds 2000$ after $N$ complete years. Find the value of $N$.
\end{enumerate}\item Mrs White invests $\pounds 1500$ in Bilbao Bank at a fixed interest rate of $1.5 \%$ per year. Mr Brown and Mrs White invest their money at the same time. The value of Mr Brown's investment will first exceed the value of Mrs White's investment after $T$ complete years.

Find the value of $T$.
\end{enumerate}

\hfill \mbox{\textit{AQA C4 2012 Q4 [8]}}