2013 RI P1 Q9

Mr Tan decides to set up a scholarship fund for worthy students. On 1 January 2013, he places this scholarship fund in a bank investment which guarantees an annual interest rate of \(2.5\%\). This interest is added to the fund at the end of each year. The annual scholarship award of \(\$2000\) is first awarded on 1 January 2014.

1. To award the scholarship for year 2014, find the minimum amount of money \(\$k\) that Mr Tan needs for the fund. If the annual scholarship is to be given out for years 2014 and 2015, show that in addition to \(\$k\), Mr Tan will need at least a further \(\$1904\), correct to the nearest dollar, for the fund.[3]
2. Find the minimum amount Mr Tan needs for the scholarship fund if he wants the annual scholarship to be given out for \(10\) consecutive years.[3]
3. Find the minimum amount Mr Tan needs for the scholarship fund if he intends to keep the scholarship going long into the future.[2]