Secondary 3 maths question?

[匿名]

2016-06-02 7:46 pm

更新1:

Sam wishes to invest $ 20000 for 2 years by considering following tw plan a : $ 20000 at 8 % p.a. Compounded half-yearly. Plan b : convert all money into British pounds at an exchange rate 1 to $ 12.50 and then deposit it at 10% p.a. Compounded yearly. Question : what should be the exchange rate after 2 years such that Sam will earn more from plan b? correct your answer to 2 decimal places. Explain your answer. Can anyone help? Don't understand how to solve this question!

更新2:

Sam wishes to invest $ 20000 for 2 years by considering following two plans. plan a : $ 20000 at 8 % p.a. Compounded half-yearly. Plan b : convert all money into British pounds at an exchange rate 1 to $ 12.50 and then deposit it at 10% p.a. Compounded yearly. Question : what should be the exchange rate after 2 years such that Sam will earn more from plan b? correct your answer to 2 decimal places. Explain your answer. Can anyone help? Don't understand how to solve this question!

回答 (1)

Lopez

2016-06-03 8:40 am

✔ 最佳答案

題目中的 $ 可能是指港幣, 請參照意見欄.
計算再修正如下.

Sol :

plan a :
r = 8% / 2 = 0.08 / 2 = 0.04
半年記息一次, 故 2 年記息 4 期.
A( plan a ) = 20000 * ( 1 + 0.04 )^4

plan b :
r = 10% = 0.1
每年記息一次, 故 2 年記息 2 期.
設 2 年後的匯率為 1英鎊兌換 k 元.
因為第 0 年換成英鎊(12.50元換 1英鎊), 第 2 年再換回原貨幣(1英鎊換 k元), 所以 :
A( plan b ) = ( 20000 / 12.50 ) * ( 1 + 0.1 )^2 * k

由題意知 A( plan b ) > A( plan a ) , 所以 :
( 20000 / 12.50 ) * ( 1 + 0.1 )^2 * k > 20000 * ( 1 + 0.04 )^4
1.1^2 * k > 12.50 * 1.04^4
k > 12.50 * 1.04^4 / 1.1^2 ≒ 12.09

Ans: 2 年後的匯率, 1英鎊至少要兌換 $12.09 以上, 他才能從 b 計畫賺得比 a 計畫更多.

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