2025 May TZ1 P1 Q3

Bob invests \(1000\) dinar in an account which pays a nominal annual interest rate of \(4\%\) compounded quarterly.
The amount of money in the account after one complete year can be written as \(1000(1 + k)^4\) where \(k \in \mathbb{Q}\).

1. Write down the value of \(k\).

   [1]

2. Expand and simplify \( (1 + x)^4\).

   [2]

3. Hence or otherwise, find the amount of money in the account after one complete year, giving your answer correct to the nearest dinar.

   [4]