MATHS FOR QUADRATIC EQUATIONS

Shirley

2011-11-19 4:54 pm

1) THE VALUE OF NEW CAR IS $ 300 000 AND ITS VALUE IS $180 000 AFTER TWO EARS. IT IS KNOWN THAT THE ANNUAL DEPRECATION RATE DECREASE GRADUALLY IF THE DIFFERENCE OF THE DEPRECATION RATE OF THE FIRST TWO YEARS IS 5% FIND THE DEPRECIATION RATE OF THE FIRST YEAR.

2) A BANK OFFER A LARGE SUM FIXED DEPOSIT PLAN OF ONE-YEAR PERIOD. THE INTEREST IS CALCULATED AND COMPOUNDED HALF-YEARLY. THE ANUUAL INTEREST RATE OF EACH 6-MONTH PERIOD INCREASE GRADUALLY.MOREWVER. THE DIFFERENCE OF THE ANUUAL INTEREST RATE OF TWO CONSECUTIVE 6 -MONTH PERIOD IS 1%. MISS WONG JOINS THE PLAN BY INVESTING $ 1 000 000. SHE RECEIVES AN AMOUNT OF 1 035 300 AFTER ONE YEAR. FIND THE ANUUAL INTEREST RATE OF THE FIRST HALF YEAR.

回答 (1)

[匿名]

2011-11-19 6:31 pm

✔ 最佳答案

1)
let y be the depreciation rate for the first year
then
1≥y≥0......a
300,000 * (1-y) * (1-y+5%) = 180,000......b
from b
20y²-41y+9=0
(5y-9) * (4y-1)=0
so y=0.25

2)
let y be the half-year interest rate
y≥0......a
1,000,000 * (1+y) * (1+y+0.01/2) = 1,035,300
10,000y²+20,500y-303=0
so y = 1.5%

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