? asked in 科學數學 · 1 decade ago

數學利率問題(英文題)?

以下四題搞不懂:

1.How much should you invest now at an annual interest rate of 5.1%

so that your balance 3years from now will be $6000 if interest is

compounded

(i)weekly(52 times a year)? (ii) continuously?

2.if $3000 is invested in a saving account that earns interest at the rate

of 5.1% compounded weekly(52 times a year) after how many fully

years will the amount at least double?

3.what annual rate compounded continuously is equivalent to an effective

rate of 5.3%?

4.if interest is compounded continuously at an annual rate of 5.1% how

many years would it take for a principle P to triple? give your answer to

the nearest year.

Update:

可以解給我看嗎?謝謝喔

1 Answer

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  • 1 decade ago
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    1.How much should you invest now at an annual interest rate of 5.1%

    so that your balance 3 years from now will be $6000 if interest is

    compounded (i)weekly(52 times a year)? (ii) continuously?

    ANSWER: 假設需投資X元。(i) compounded weekly: X*(1+ 5.1%/52)52*3 = 6000,X = 5149.16;(ii) compounded continuously: X*e5.1%*3 = 6000,X = 5148.78。

    2.if $3000 is invested in a saving account that earns interest at the rate

    of 5.1% compounded weekly(52 times a year) after how many fully

    years will the amount at least double?

    ANSWER: 假設需投資T年。3000*(1+ 5.1%/52)52*T = 6000,得到T=13.59年,即14年。

    3.what annual rate compounded continuously is equivalent to an effective rate of 5.3%?

    ANSWER: 假設利率為I。eI = 1.053,得到I = 5.1643%。

    4.if interest is compounded continuously at an annual rate of 5.1% how

    many years would it take for a principle P to triple? give your answer to

    the nearest year.

    ANSWER: 假設需要T年,本金會成為3倍。P * e5.1%*T = 3P,得到T = 21.54年,即22年。

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