✔ 最佳答案
20) Let x% be the dep. rate of the first year, then (x + 5)% will be the dep. rate of the second year. Hence:
300000 (1 - x/100) [1 - (x + 5)/100] = 180000
30 (100 - x) (95 - x) = 180000
x2 - 195x + 9500 = 6000
x2 - 195x + 3500 = 0
(x - 175)(x - 20) = 0
x = 175 (rej.) or 20
So the dep. rate of the first year is 20%.
21) Let the interest rate be x%, then:
[20000 (1 + x/100)2 - 20000] - 20000(2x/100) = 30
2(100 + x)2 - 20000 - 400x = 30
2x2 = 30
x = 3.87
So the interest rate is 3.87%
22) Let x% be the annual rate of the first half year, then (x + 1)% will be the rate of the second half year.
So:
1000000 (1 + x/200) [1 + (x + 1)/200] = 1035300
25 (200 + x)(201 + x) = 1035300
x2 + 401x + 40200 = 41412
x2 + 401x - 1212 = 0
(x + 404)(x - 3) = 0
x = -404 (rej.) or 3
Hence the annual interest rate for the first half year is 3%