Financial Maths, STD1 2026 HSC 30

An amount of $3500 is invested for 3 years at an interest rate of 5.75% per annum, compounded annually.

Find the simple interest rate per annum that will give the same future value. Give your answer as a percentage, correct to 2 decimal places. (4 marks)

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$6.09\%$

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$FV$	$=PV(1+r)^n$
	$=3500(1+0.0575)^3$
	$=\$4139.13$

$\text{Interest earned}=4139.13-3500=\$639.13$

$\text{Using}\ \ I=Prn:$

$639.13$	$=3500\times r\times 3$
$r$	$=\dfrac{639.13}{10\ 500}$
	$=0.06087…$
	$=6.09\%\ \text{(2 d.p.)}$

\(FV\)	\(=PV(1+r)^n\)
	\(=3500(1+0.0575)^3\)
	\(=\$4139.13\)

\(639.13\)	\(=3500\times r\times 3\)
\(r\)	\(=\dfrac{639.13}{10\ 500}\)
	\(=0.06087…\)
	\(=6.09\%\ \text{(2 d.p.)}\)