maths~~~~~~~~

用戶7639

2010-04-06 7:17 am

慧玲參加了銀行的一個十年儲存款計劃,計劃訂明年利訊為10%,每年計算複利息一次。若她需在每年年初存入$10000,當10年期滿可得到的本利和是多少？(答案須準確至最接近的元。)

回答 (1)

用戶10012

2010-04-06 6:45 pm

✔ 最佳答案

Beginning of 1st year amount = 10,000
Beginning of 2nd year amount = 10,000(1 + 10%) + 10,000
Beginning of 3rd year amount = [10,000(1 + 10%)](1 + 10%) + 10,000(1 + 10%) + 10,000 = 10,000(1 + 10%)^2 + 10,000(1 + 10%) + 10,000.
so beginning of 10th year = 10,000(1.1)^9 + 10,000(1.1)^8 + .... + 10,000(1.1) + 10,000
at end of 10th year = 10,000(1.1)^10 + 10,000(1.1)^9 + ... + 10,000(1.1)^2 + 10,000(1.1)
= 10,000(1.1)[(1.1)^9 + (1.1)^8 + (1.1)^7 + (1.1)^6 + ..... + 1.1 + 1]
which is a G.S. with a = 1, r = 1.1 and n = 10
= 10,000(1.1)[(1.1)^10 - 1]/(1.1 - 1) = 110,000[(1.1)^10 - 1]= 110,000(1.59374)
= 175312 = total amount.

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