問f.2幾題數~percentage~10points~!

1)What is the increase in interest for saving $10000 in a bank at a compound interest of 20% p.a. for two years,if the interest is compounded half-yearly instead of annually?

Increase in interest
= $10000(1 + 20%/2)2x2 + $10000(1 + 20%)2
= $10000(1.1)4 + $10000(1.2)2
= $(14641 - 14400)
= $241


2)What is the difference between simple interest and compound interest(compounded annually) at 4% p.a. for 2years with a principal of $20000?

Difference between simple interest and compound interest
= $20000(1 + 4%)2 - $20000(1 + 2x4%)
= $20000(1.04)2 - $20000(1.08)
= $(21632 - 21600)
= $32


3)At what simple interest rate will a sum of money triple itself in 20 years?

Let R% be the interest rate.
Let P be the principal.

P(1 + 20xR%) = 3P
1 + 0.2R = 3
0.2R = 2
R = 10

Simple interest rate = 10%


4)The population of a city increase steadily at 4% every year.If the present population is 250000,find its population after 3 years.Give your answer correct to the nearest thousand.

Population after three years
= 250000(1 + 4%)3
= 250000(1.04)3
= 281216
≈ 281000 (to the nearest thousand)


5)A tree is now 6.76m high.Two years ago it was 4m high.If the tree grows at a constant rate every year,what is the annually growth rate?

Let R% be the growth rate.
4(1 + R%)2 = 6.76
(1 + R)2 = 1.69

Since 1 + R > 0
then (1 + R%) = 1.3
R% = 0.3
R% = 30%

The annually growth rate = 30%


6)A man put $10 into a bank at the beginning of 1900 at a compound inerest of 8%per annum,compounded annually.How much can he get back at the end of 2003?(Correct the answer to nearest cent.)

No. of years
= [(2003 - 1900) + 1] years
= 104 years

The sum that he can get back
= $10(1 + 8%)104
= $10(1.08)104
= $29927.51


Vocab~要中文解釋plz
1)interest - 利息
2)compound interest - 複利息/複利
3)p.a. - 每年 (全寫是 per annum)
4)annually - 每年的
5)simple interest - 單利息/單利
6)triple - 三倍
7)constant rate - 固定利率
8)annual growth rate - 每年生長率
9)per annum - 每年 (簡寫是 p.a.)
10)compounded annually - 每年複利一次