2025 ACJC P1 Q12

Sarah, a Singaporean Citizen, started a \(4\)-year undergraduate Computing course at the National University of Singapore (NUS) in August \(2021\). The annual tuition fee, after the MOE Tuition Grant, is $\(8250\). Sarah took a Tuition Fee Loan (TFL) covering \(90\)% of her tuition fees. This loan is interest-free during her course of study.

Sarah decided to set aside \(\(x\) per month from August \(2021\). This amount is increased by \(\\)2\) each subsequent month. (Sarah set aside \(\(x\) in August \(2021\), \)\((x + 2)\) in September \(2021\), ...) With the amount set aside, she repaid one-fifth of her total TFL at the end of July \(2025\).

1. Find the value of \(x\).[3]

Upon Sarah's graduation, the TFL's interest rate becomes effective at a fixed rate of \(0.4\)% per month, calculated on the outstanding balance at the end of the month. The interest is first charged on \(31\)st August \(2025\).

Sarah plans to make monthly repayments of $\(y\) to the bank on the \(1\)st of every month, starting from \(1\)st September \(2025\).

2. Find the amount of outstanding loan after Sarah's first monthly repayment.[1]
3. Show that the amount of outstanding loan after Sarah's \(n\)th monthly repayment is \(23760(1.004)^n - 250y(1.004^n - 1)\).[3]
4. Sarah wants to pay off her remaining loan by the end of \(3\) years. Find the value of \(y\).[2]

Sarah decided on a different repayment strategy. For the first \(24\) months, she repays \(\(500\) per month. After these \(24\) months, she doubles her monthly repayment to \(\\)1000\).

5. Determine the month and year Sarah will clear her loan and calculate the amount of her final repayment.[4]