Question

求助!!经济数学!!

第一条:You want to buy a TV and you face the following choices:
i) Buy TV at the store using a bank loan. There is no down payment as the bank can take your TV if you default on the loan. The loan is at the annual market rate of 5%. and the loan amount is $2000 to be repaid monthly over 4 years.
(ii) Rent-to-buy from the same store. The monthly rental is $120 for 48 months andthen you pay $1,000 to own the TV.

Which is the cheapest option and what is the present value of its net cost?

第二条: After visiting your car dealers, doing your research on the best leases available, you have three options.
(i) Purchase the car for cash and receive a $1,000 cash rebate from Dealer A. The price of the car is $10,000.
(ii) Lease the car from Dealer B. Under this option, you pay the dealer $500 now and $200 a month for each of the next 36 months (the first $200 payment occurs 1 month from today). After 36 months you pay $8,000 to own the car.
(iii) Purchase the car from Dealer C who will lend you the entire purchase price of the car for a zero interest 36-month loan with monthly payments. The car price is $10,000.Suppose the market interest rate is 6%.

What is the net cost today of the above three options? Which option offers you the cheapest financing?

请问应该要怎样做呀?!!

Answer 1

先翻一下：

第一条：你想要买一台电视机，有以下两个选择：

i) 在商店通过银行贷款的方式买这台电视机。这种方式不需要首付，不过如果你付不起后期的分期付款的话银行就会把你的电视机拿走。银行贷款的年利率为5%，贷款额2000，需要在今后4年中每个月分期还清。
ii) 用先租后买的融资租赁方式从这家商店购买者台电视机。月租金为120，需要连续租借48个月，然后再支付1000元购买这台电视机。

哪种方式是最便宜的？这种支付方式的现值是多少？

这道题就是求分别现值：
i) PV = 2000
ii) PV = 120*(P/A: 5%/12, 48) + 1000*(P/F: 5%, 4) = $6,029.83

所以，你应该选择银行贷款方式。

第二条：在约见你的汽车经销商之后，你有3种方式可以买一辆汽车：

i) 用10,000元现金买下这辆车之后，就可以从A经销商获得1000元的现金返还。
ii) 从B经销商租用这辆车，你只需要现在支付500元，然后每月支付200元，连续支付36个月，然后你再支付8000元就可以拥有这辆车。
iii) 从C经销商贷款10,000买下这辆车，C经销商可以提供给你36个月的免息贷款。
假设市场利率为6%

以上3种方式中各个方式支付额的现值是多少？哪种方式是最便宜的？

i) PV = 10000-1000 = 9000
ii) PV = 500 + 200*(P/A: 6%/12, 36) + 8000*(P/F: 6%, 3) = $13,259.36
iii) PV = 10,000/36*(P/A: 6%/12, 36) = $9,130.84

所以，你应该选择第一个经销商。

希望帮到了你，满意请点击“选为满意答案”及时采纳，谢谢!

追问

我想问如果是要用
PV= FV/(1+r)t
或
PV=C*[[1-1/(1-r)t]/r]
这2条算式应该要怎样计算?
因为我不明白(P/A: 6%/12, 36)这种计算, 好像还没有学

而且我想问第一条的(i), 如何知道是PV=2000??

追答

PA就是你说的n个 PV= FV/(1+r)t 这个等比数列求和。例如第一条中的ii) 120*(P/A: 5%/12, 48) 就是120 / (1+5%/12)^1 +120 / (1+5%/12)^2+......+120 / (1+5%/12)^48

建议你用专用的金融计算器算这个数列，或者用电脑上的Excel的=PV()这个函数。实在不行的话就只能按等比数列求和公式Sn=a1(1-q^n)/(1-q) 用普通计算器算这个数列了。

第一条的(i), 根据：The loan is at the annual market rate of 5%. and the loan amount is $2000 to be repaid monthly over 4 years 直接得出PV=2000

Answer 2

先翻译一下吧。。。太多唔想睇。。。