# Maths,sequence(hurry)

Mr.Chan deposits \$2000 at the beginning of each mouth at an interest rate of 4% p.a.,compounded mouthly for 1.5 years

1. Find the amount Mr.Chan got after 1.5 years

2 If he want to obtain \$100000 after 1.5 years, how much should he deposit each mouth?

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The answer is \$37162(i,e, earning \$1162)for (1)and \$5382 for(2),but I don&#39;t know how to work it out,can anyone help?

### 1 個解答

• 最佳解答

Mr.Chan deposits \$2000 at the beginning of each mouth at an interest rate of 4% p.a.,compounded mouthly for 1.5 years

1. Find the amount Mr.Chan got after 1.5 years

他第一個月存的錢18個月(1.5年)的本利和

2000(1+4%/12)18

第二個月

2000(1+4%/12)17

…….

所以18月的總本利和為

2000(1+4%/12)18 + 2000(1+4%/12)17 + …. + 2000(1+4%/12)1

這是一個幾何級數，

所以本利和為

2000(1+4%/12)[(1+4%/12)18– 1] / (4%/12)

= 37161.8元

2 If he want to obtain \$100000 after 1.5 years, how much should he deposit each mouth?

有兩種求法，

方法1)因每月存款會和最後的本利和成正比，所以可用比例計

x / 2000 = 100000 / 37161.8

x = \$5381.9

方法1)

直接由原有公式計

若本利和為A，每月存款為P，每月的利率為r%(r% = 4%/12)，總供款期數為N

A = P(1+r%)[(1+r%)n – 1]/r%

P = Ar%/{(1+r%)[(1+r%)n – 1]}

P = 100000(4%/12)/{(1+4%/12)[(1+4%/12)n – 1]}

P = \$5381.9

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