※ 引述《jaychouyo (˙˙˙)》之銘言：
: 今天做ASM study manual FM 的題目如下：
: Jason deposits 3960 into a bank account at t = 0. The bank credits interest
: at the end of each year at a force of interest (delta) = 1/(8+t). Interest
: can be reinvested at an annual effective rate of 7%.
: The total accumulated amount at time t = 3 is equal to X. Caculate X.
: (A) 5394 (B) 5465 (C) 5551 (D) 5600 (E) 5685
: 答案是(A)，解答如下：
: a(t) = (8+t)/8
: i[t] = [a(t)/a(t-1)] -1 = 1/(7+t)
: Interest earned each year:
: 3960*i[1] = 3960*(1/8) = 495
: 3960*i[2] = 3960*(1/9) = 440
: 3960*i[3] = 3960*(1/10) = 396
: AV = 3960 + 495(1.07)^2 + 440(1.07) + 396 = 5393.53
: 原本的想法是覺得因為
: a(t) = (8+t)/8 = 1 + t/8
: 所以就把他當成是 simple interest 的給息方式 ( i = 1/8 )
: 因此每年的 interest earned 都是
: 3960*(1/8) = 495
: AV = 3960 + 495*(s3 angle 0.07) = 5551.37
: 剛好答案(C)也有這個數字...
: 想請問一下，這樣的想法是不是哪邊有錯誤?
: 若是往後又遇到 a(t) 的形式是 simple interest 的樣子，
: 能夠把他當成 simple interest 下去做嗎? 謝謝!
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