F.6 Math's Q (Sum of AS/ GS)

呢啲加奶

2013-10-27 12:57 am

1. Find the sum of the series (2+log2) + (4+log4) + (8+log8) + ‧‧‧to
10 terms. (Ans: 2046 + 55 log2) 這條是否可以利用 2^n + log2^n 來計

2. Nelson has the following money-saving plan:
Staring from 1st January 2010, I will save $x in the bank in the beginning of
every 6-month period until 31st December 2019.

It si given that the interest rate is fixed at 6%p.a., compounded half-yearly. 這裡是否用3%來計

(a) Find, in terms of x,

(i) the sum that the first 3 deposits will amount to just after 31st December
2019, [Ans: $x(1.03^20 + 1.03^19 + 1.03^18)] 20,19,18是甚麼??

(ii) the total amount he will get just after 31st December 2019.
[Ans: $103x(1.030^20 -1 ) ÷3]

(b) If Nelson wants to have $500000 just after 31st December 2019, find the
value of x. (ans:18066)

回答 (1)

myisland8132

2013-10-27 5:55 am

✔ 最佳答案

1 (2+log2) + (4+log4) + (8+log8) + ‧‧‧to
10 terms

= 2 + 4 + 8 ... + 2^10 + log2 + 2log2 + 3log2 + ... + 10log2

= 2046 + 55log22(a)(i) Sum of the first 3 deposits will amount to just after 31st December
2019

= x(1.03^20 + 1.03^19 + 1.03^18)

因為是每半年複利一次﹐所以是3%。第一次的存款到2019年12月31日共有20期﹐所以是20次方。

(ii) the total amount he will get just after 31st December 2019

= x(1.03^20 + 1.03^19 + 1.03^18 + ... + 1.03)

= 1.03x(1.03^20 - 1)/(1.03 - 1)

= 103x(1.03^20 - 1)/3

(b) 103x(1.03^20 - 1)/3 = 500000

103x(0.806111) = 1500000

x = 18066

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