| Category | Assignment | Subject | Mathematics |
|---|---|---|---|
| University | Singapore University of Social Sciences (SUSS) | Module Title | MTH105 Fundamentals of Mathematics |
| Assessment Type | Tutor-Marked Assignment |
|---|
(b) In January 2021, John borrowed $29,000 from a bank for his further studies. The outstanding loan balance incurs a compound interest 5% per year. The interest charged is calculated and the outstanding balance is updated on the last day of each year.
John plans to pay back a fixed amount of $x on the first day of each month, starting from the first month after his graduation. John will graduate from his study at the end of 2024 and will make his first payment on 1st January 2025.
Show that the amount owed on the last day of 2025 after the interest is added is 1.045 (29000) 1.045(12 and find the minimum amount, correct to the nearest dollar, that John must pay each month, if he wishes to complete paying the loan by the end of December 2032. (11 marks)
Use the Euclidean Algorithm to determinedgcd (14973, 474 and express as an integral linear combination of 14973 and 4746. (10 marks)
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