一款游戏设备的现金价格为 $710。 乔琳（Jolene）以分期付款（租购）方式购买该游戏设备，并支付 30% 的首付款。 以下是金融公司向她提供的不同分期付款方案，还款期均为 5 年。 方案 A：年复利 2.5% 方案 B：年单利 2.6% 请通过清晰的数学计算过程进行说明和论证，乔琳应该选择哪种分期付款方案。 答

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.