The cash price of a gaming device is $710. Jolene buys this gaming device on hire purchase and pays a 30% deposit. The following shows the different hire purchase schemes with a repayment period of 5 years that are offered to her by the finance company. Scheme A: Compound interest of 2.5% per annum Scheme B: Simple interest of 2.6% per annum Explain and justify, with clear mathematical working, which hire purchase scheme should Jolene take up. Answer

1. Find the deposit and the amount financed

Deposit paid:
$30\% \times 710 = 0.30 \times 710 = \$213$
Amount financed:
$710 - 213 = \$497$

2. Calculate the repayment amount under Scheme A using compound interest

Scheme A uses compound interest of $2.5\%$ per annum for 5 years.
$\text{Amount} = 497(1+0.025)^5$
$= 497(1.025)^5$
$= \$562.81 \text{ approximately}$

3. Calculate the repayment amount under Scheme B using simple interest

Scheme B uses simple interest of $2.6\%$ per annum for 5 years.
$\text{Amount} = 497\left(1+0.026\times 5\right)$
$= 497(1.13)$
$= \$561.61$

4. Find the total amount payable for each scheme including the deposit

Scheme A total payable:
$213 + 562.81 = \$775.81$
Scheme B total payable:
$213 + 561.61 = \$774.61$

5. Compare both schemes and justify the choice

Difference:
$775.81 - 774.61 = \$1.20$
Since Scheme B costs less, Jolene should take up Scheme B.