Financial Maths, STD2 2020 HSC 22 (Adapted)

Diego pays a $600 car repair bill using his credit card. The card charges interest at 18.6% per annum, compounded daily, and has no interest-free period.

Twenty days after the purchase, Diego makes a part-payment of $300.

Determine how much Diego still owes after making the $300 part-payment. (3 marks)

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$\text{Amount owing}=\$306.14$

Show Worked Solution

$\text{Days of interest}\ (n)=20$

$\text{Daily interest rate}\ (r)=\dfrac{18.6\%}{365}=\dfrac{0.186}{365}=0.00050959\ldots$

$\text{Amount owing}\ (FV)$	$=PV(1+r)^n-300$
	$=600(1+0.00050959\ldots)^{20}-300$
	$=606.14-300$
	$=\$306.14$

\(\text{Amount owing}\ (FV)\)	\(=PV(1+r)^n-300\)
	\(=600(1+0.00050959\ldots)^{20}-300\)
	\(=606.14-300\)
	\(=\$306.14\)