匿名
匿名 發問於 科學及數學數學 · 8 年前

S3 math!!!

(1)a new car is worth $250 000 and its depreciation rate is 30% for the first year and 20% for every subsequent year

(a) find its value 3 years later

(b) find the overall percentage change in its value over these 3 years

(2) jack deposits $80 000 in a bank at 6% p.a. for 2 year. find the mount obtained if the interest is compounded

(a) quarterly

(b) monthly

更新:

第2題打錯了!!!應該是

(2) jack deposits $80 000 in a bank at 6% p.a. for 1 year. find the amount obtained if the interest is compounded

(a) quarterly

(b) monthly

更新 2:

第2題(give your answers correct to the nearet $1)

2 個解答

評分
  • Adam
    Lv 7
    8 年前
    最愛解答

    (1)

    (a)

    The value of the car 3 years later

    = $250 000 x (1 - 30%) x (1 - 20%)²

    = $112 000

    (b)

    Overall percentage change

    = [(112 000 - 250 000)/250 000] x 100%

    = -55.2%

    (decrease 55.2%)

    =====

    (2)

    (a)

    Principal, P = $80 000

    Interest rate, R% = 6%/4 = 1.5%

    No. of periods, n = 2 x 4 = 8

    Amount, A

    = P (1 + R%)^n

    = $80 000 x (1 + 1.5%)^8

    = $90 119.41 (to 2 decimal places)

    (b)

    Principal, P = $80 000

    Interest rate, R% = 6%/12 = 0.5%

    No. of periods, n = 2 x 12 = 24

    Amount, A

    = P (1 + R%)^n

    = $80 000 x (1 + 0.5%)^24

    = $90 172.78 (to 2 decimal places)

    2012-12-26 22:48:44 補充:

    (2)(a)

    Amount, A = $90 119 (to the nearest dollar)

    (2)(b)

    Amount, A = $90 173 (to the nearest dollar)

    2012-12-26 22:55:40 補充:

    (2)

    If it is 1 year instead of 2 years, the solutions are :

    (a)

    Principal, P = $80 000

    Interest rate, R% = 6%/4 = 1.5%

    No. of periods, n = 4

    Amount, A

    = P (1 + R%)^n

    = $80 000 x (1 + 1.5%)^4

    = $84 909 (to the nearest dollar) ...... ans

    2012-12-26 22:55:52 補充:

    (b)

    Principal, P = $80 000

    Interest rate, R% = 6%/12 = 0.5%

    No. of periods, n = 12

    Amount, A

    = P (1 + R%)^n

    = $80 000 x (1 + 0.5%)^12

    = $84 934 (to the nearest dollar) ...... ans

    資料來源: Adam, Adam, Adam
  • 8 年前

    1a)

    Its value

    =250,000(1-30%)(1-20%)^2

    =$112,000

    1b)

    The change

    =(112,000-250,000)/250,000 x 100%

    = -55.2%

    Thus, the value decreased by 55.2%

    2a)

    Amount

    =80,000[1+(6%/4)]^4

    =$84,909, corr to the nearest $1

    2b)

    Amount

    =80,000[1+(6%/12)]^12

    =$84,934, corr. to the nearest $1

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