2022 RI Promo Q12

On 1 Jan 2023, Sam takes an interest-free study loan of \(\$28\,000\) from his parents for his university fees. He starts to repay \(\$m\) to his parents on 1 Feb 2023 and progressively increases \(\$50\) in his repayment amount at the start of each subsequent month.

1. Given that \(m=500\), on which date will Sam finish repaying his parents?[4]
2. If Sam wants to finish repaying his parents by the end of 2024, find the minimum value of \(m\), giving your answer to the nearest dollars.[3]

On 1 Jan 2023, Sam’s friend, Joshua, takes a study loan of \(\$28\,000\) from UAB Bank. The bank charges an interest rate of \(0.2\%\) per month at the end of each month from the start of the loan period.

3. Given that he repays \(\$500\) to the bank on the first day of every month beginning from 1 Feb 2023 onwards, on which date will Joshua finish repaying his study loan?[5]