# 2013 RI P1 Q9

## Timothy Gan

This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.
##### 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. (i) 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]

(ii)

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]

(iii)

Find the minimum amount Mr Tan needs for the scholarship fund if he intends to keep the scholarship going long into the future.

[2]

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