Emily 正在考虑办理一张新的信用卡，并筛选出了三个选项：卡 A、卡 B 和卡 C。每张卡提供不同的权益、奖励，并收取不同的年费。 下表展示了每张卡的主要特征：

1. Calculate the first-month cashback for each card from the SGD 2000 expenditure.

Card A cashback: $1.5\% \times 2000 = 0.015 \times 2000 = 30$

Card B cashback: $1.3\% \times 2000 = 0.013 \times 2000 = 26$

Card C cashback: $1.2\% \times 2000 = 0.012 \times 2000 = 24$

2. Add the sign-up bonus to the cashback to find the net rewards for each card.

Card A net rewards: $30 + 50 = 80$

Card B net rewards: $26 + 60 = 86$

Card C net rewards: $24 + 70 = 94$

1. Calculate the total expenditure and cashback for 12 months using Card A.

Monthly expenditure $= \char36{}2000$

Total expenditure for 12 months:
$12 \times 2000 = \$24000$

Card A cashback per month:
$1.5\% \times 2000 = 0.015 \times 2000 = \$30$

Total cashback for 12 months:
$12 \times 30 = \$360$

2. Subtract the total rewards and include the annual fee to find the amount payable after the first year.

Sign-up bonus for Card A $= \char36{}50$

Annual fee for Card A $= \char36{}110$

Total amount payable:
$24000 + 110 - 360 - 50 = 23700$

1. Find Emily's total card expenditure over two years, excluding annual fees and lounge access passes.

Monthly card expenditure $= \char36{}2000$

For 2 years, there are $24$ months.

$24 \times 2000 = 48000$

Total expenditure over 2 years $= \char36{}48000$.

2. Calculate the total cashback over two years and include the sign-up bonus for each card.

Card A:

$1.5\% \times 48000 = 720$

Total rewards for Card A:

$720 + 50 = 770$

Card B:

$1.3\% \times 48000 = 624$

Total rewards for Card B:

$624 + 60 = 684$

Card C:

$1.2\% \times 48000 = 576$

Total rewards for Card C:

$576 + 70 = 646$

3. Calculate the total annual fees over the two years for each card.

Card A annual fees over 2 years:

$2 \times 110 = 220$

Card B annual fees over 2 years:

$2 \times 90 = 180$

Card C annual fees over 2 years:

$0 + 250 = 250$

This is because Card C's annual fee is waived for the first year and is $250 from the second year onwards.

4. Calculate the cost of additional airport lounge access passes needed over two years.

Emily needs $5$ airport lounge access passes per year.

Card A gives $2$ free passes per year, so extra passes needed per year:

$5 - 2 = 3$

Over 2 years, cost of extra passes for Card A:

$3 \times 2 \times 50 = 300$

Card B gives $4$ free passes per year, so extra passes needed per year:

$5 - 4 = 1$

Over 2 years, cost of extra passes for Card B:

$1 \times 2 \times 50 = 100$

Card C gives unlimited free passes, so extra cost:

$\$0$

No cashback is earned on the amount spent on airport lounge access passes.

5. Find the total amount payable over two years for each card after subtracting rewards and adding fees and extra lounge pass costs.

Total amount payable:

$\text{total expenditure} + \text{annual fees} + \text{extra lounge pass cost} - \text{total rewards}$

Card A:

$48000 + 220 + 300 - 770 = 47750$

Card B:

$48000 + 180 + 100 - 684 = 47596$

Card C:

$48000 + 250 + 0 - 646 = 47604$

6. Compare the totals and justify the best choice considering Emily's travel preference.

Comparing the total amounts payable:

$\$47596 < \$47604 < \$47750$

Card B has the lowest total amount payable, but it provides only $4$ free lounge passes per year, so Emily must still buy $1$ extra pass per year.

Card C costs only

$47604 - 47596 = 8$

more than Card B over 2 years, and it gives unlimited airport lounge access passes.

Since travel perks are important to Emily, Card C might be the best choice.