In January 2001, John borrowed $\$29\mathrm{}000$ from a bank. Interest was charged at $4.5\%$ per y

Question

In January 2001, John borrowed $\$29\mathrm{}000$ from a bank. Interest was charged at $4.5\%$ per year and was calculated at the end of each year starting from 2001. John planned to pay back a fixed amount of $\$x$ on the first day of each month, starting from the first month after his graduation. John graduated from his study in at the end of 2004 and started payment in January 2005. Show that the amount owed at the end of 2005 was ${{1.045}^{5}}(29000)-1.045(12x)$. [1] Taking 2005 as the first year, find an exact expression for the amount John owed at the end of the $n$th year, simplifying your answer in terms of $n$ and $x$. [3] If the loan must be repaid within $8$ years from John’s graduation, find the minimum amount, correct to the nearest dollar, John must pay each month. [2]

Accepted Answer

(b)(i) $29000(1.045)^{n+4} - \frac{836}{3}x(1.045^n - 1)$; (b)(ii) $\$419$

2015 SRJC P1 Q10

2015 SRJC P1 Q10

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