Financial Maths, STD2 2025 HSC 34 (Adapted)

The table shows future value interest factors for an annuity of $1.

Larry invests a single amount of $18 000 for 5 years at 9% per annum, compounding monthly.

Tobias wants to end up with the same amount as Larry by using an annuity. He will pay a fixed sum into an account at the end of each month for 5 years, with the account also paying 9% per annum, compounding monthly.

Using the table, work out how much Tobias must deposit each month. (3 marks)

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$\$373.65$

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$r=\dfrac{0.09}{12}=0.0075,\ \ n=12\times 5=60$

$\text{Larry’s investment:}$

$FV=18\,000(1+0.0075)^{60}=28\,182.26$

$\text{Tobias’s investment:}$

$\text{Annuity factor:}\ 75.42414$

$\text{Annuity}\times 75.42414$	$=\$28\,182.26$
$\text{Annuity}$	$=\dfrac{28\,182.26}{75.42414}=\$373.65$

\(\text{Annuity}\times 75.42414\)	\(=\$28\,182.26\)
\(\text{Annuity}\)	\(=\dfrac{28\,182.26}{75.42414}=\$373.65\)