F4 maths 一元二次複利率..

2010-10-08 4:01 am

A bank offers a large sum fixed deposit plan of one-year period.The interest is

calculated and compounded half-yearly.The annual interest rate for each

6-month period increase gradually.Moreover,the difference of the annual interest

rates of two consecutive 6-month period is 1%.Miss Wong joins the plan by

investing $1 000 000.She receives an amount of $1035300 after one year.

Find the annual interest rate for the first half year.

回答 (1)

Yogi

2010-10-08 5:18 am

✔ 最佳答案

你好～～～

以下都是本人的一些意見而已，如有錯誤請多多指教～

Solution:

Let the annual interest rate for the first half year be y%.

1000000(1 + y%/2)[1 + (y + 1)%/2] = 1035300

(1 + y/200)[1 + (y + 1)/200] = 1035300 / 1000000

1 + (y + 1) / 200 + y / 200 + [y(y + 1)] / 40000 = 1.0353

200(2y + 1) + y^2 + y = 1412

400y + 200 + y^2 + y - 1412 = 0

y^2 + 401y - 1212 = 0

(y - 3)(y + 404) = 0

y = 3

So, the annual interest rate for the first half year is 3%.

希望可以幫到你～～～～～

2010-10-08 18:22:13 補充：
對不起，好像打漏了些東西︰

「(y - 3)(y + 404) = 0

y = 3 or y = -404(rejected)」

參考: Yogi

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