數條英數題(中二級)(列式)

2009-07-10 4:13 pm

1,Three positive number are in the ratio 3:4:5.If the difference between the largest number and the smallest is 10.Find the numbers.
2,What is the increase in interest for saving $10000in a bank at a compound interest of 20%p.a.for two years.if the interest is compounded half-yearly interest of annually?
3,What is the difference between simple interest and compound interest(compounded annually)at4%p.a.for2years with a principal of $20000?
4,At what simple interest rate will a sum of money triple itself in two years?
5,A tree is now 6.76m high.Two years ago it was 4m high.If the tree grows at a constant rate each year,what is the annual growth rate?
6,A man put $10into a bank at the beinning of1900 at a interest of8%per annum,compounded annually.How much can he get back at the end of 2003?(Corr to the nearest cent)

回答 (1)

用戶10012

2009-07-10 5:19 pm

✔ 最佳答案

1.
Let the smallest no. be 3k, the other no. will be 4k and 5k.
so 5k - 3k = 10
2k = 10, k = 5
so the nos. are 15, 20 and 25.
2.
Amount for annually = 10,000(1 + 20%)^2 = 10,000(1.2)^2.
Amount for half-yearly = 10,000( 1 + 20%/2)^4 = 10,000(1.1)^4
Difference in interest = 10,000(1.1)^4 - 10,000(1.2)^2
= 10,000(1.4641 - 1.44) = $241.
3.
Amount in compound int. = 20,000(1 + 4%)^2 = 20,000(1.04)^2 = 21632.
Therefore int. = 1632
Interest in simple int. = 20,000(2)(0.04) = 1600
Difference = $32.
4. Let principle = P
so interest = 3P - P = 2P in 2 years.
so 2P = P(r)(2)
r = 1 = 100%
5.
Let annual growth rate = r
so 4(1 + r)^2 = 6.76
(1 + r)^2 = 1.69
1 + r = sqrt 1.69 = 1.3
r = 0.3 = 30%.
6.
Amount he gets back = 10(1 + 8%)^(2003 - 1900 + 1)
= 10(1.08)^104
= $29927.51

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