<p>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 $$8250$. Sarah took a Tuition Fee Loan (TFL) covering $90$% of her tuition fees. This loan is interest-free during her course of study.</p>
<p>Sarah decided to set aside $$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 $2025$.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the value of $x$.</span><span class="inline-marks">[3]</span></div></li></ol>
<p>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 $2025$.</p>
<p>Sarah plans to make monthly repayments of $$y$ to the bank on the $1$st of every month, starting from $1$st September $2025$.</p>
<ol class="abc-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Find the amount of outstanding loan after Sarah's first monthly repayment.</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Show that the amount of outstanding loan after Sarah's $n$th monthly repayment is $23760(1.004)^n - 250y(1.004^n - 1)$.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Sarah wants to pay off her remaining loan by the end of $3$ years. Find the value of $y$.</span><span class="inline-marks">[2]</span></div></li></ol>
<p>Sarah decided on a different repayment strategy. For the first $24$ months, she repays $$500$ per month. After these $24$ months, she doubles her monthly repayment to $\$1000$.</p>
<ol class="abc-list" start="5"><li><div class="list-item-content"><span class="list-item-text">Determine the month and year Sarah will clear her loan and calculate the amount of her final repayment.</span><span class="inline-marks">[4]</span></div></li></ol>

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 $2025$.

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 $2025$.

Find the amount of outstanding loan after Sarah's first monthly repayment.

Show that the amount of outstanding loan after Sarah's $n$th monthly repayment is $23760(1.004)^n - 250y(1.004^n - 1)$.

Sarah wants to pay off her remaining loan by the end of $3$ years. Find the value of $y$.

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$.

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

2025 ACJC P1 Q12

2025 ACJC P1 Q12