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KYO Oscar 發問於 科學及數學數學 · 1 十年前

Maths,sequence(hurry)

Mr.Chan deposits $2000 at the beginning of each mouth at an interest rate of 4% p.a.,compounded mouthly for 1.5 years

1. Find the amount Mr.Chan got after 1.5 years

2 If he want to obtain $100000 after 1.5 years, how much should he deposit each mouth?

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The answer is $37162(i,e, earning $1162)for (1)and $5382 for(2),but I don't know how to work it out,can anyone help?

1 個解答

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  • 1 十年前
    最愛解答

    Mr.Chan deposits $2000 at the beginning of each mouth at an interest rate of 4% p.a.,compounded mouthly for 1.5 years

    1. Find the amount Mr.Chan got after 1.5 years

    他第一個月存的錢18個月(1.5年)的本利和

    2000(1+4%/12)18

    第二個月

    2000(1+4%/12)17

    …….

    所以18月的總本利和為

    2000(1+4%/12)18 + 2000(1+4%/12)17 + …. + 2000(1+4%/12)1

    這是一個幾何級數,

    所以本利和為

    2000(1+4%/12)[(1+4%/12)18– 1] / (4%/12)

    = 37161.8元

    2 If he want to obtain $100000 after 1.5 years, how much should he deposit each mouth?

    有兩種求法,

    方法1)因每月存款會和最後的本利和成正比,所以可用比例計

    x / 2000 = 100000 / 37161.8

    x = $5381.9

    方法1)

    直接由原有公式計

    若本利和為A,每月存款為P,每月的利率為r%(r% = 4%/12),總供款期數為N

    A = P(1+r%)[(1+r%)n – 1]/r%

    P = Ar%/{(1+r%)[(1+r%)n – 1]}

    P = 100000(4%/12)/{(1+4%/12)[(1+4%/12)n – 1]}

    P = $5381.9

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