# 數學利率問題(英文題)?

1.How much should you invest now at an annual interest rate of 5.1%

so that your balance 3years from now will be \$6000 if interest is

compounded

(i)weekly(52 times a year)? (ii) continuously?

2.if \$3000 is invested in a saving account that earns interest at the rate

of 5.1% compounded weekly(52 times a year) after how many fully

years will the amount at least double?

3.what annual rate compounded continuously is equivalent to an effective

rate of 5.3%?

4.if interest is compounded continuously at an annual rate of 5.1% how

many years would it take for a principle P to triple? give your answer to

the nearest year.

Update:

Rating

1.How much should you invest now at an annual interest rate of 5.1%

so that your balance 3 years from now will be \$6000 if interest is

compounded (i)weekly(52 times a year)? (ii) continuously?

ANSWER: 假設需投資X元。(i) compounded weekly: X*(1+ 5.1%/52)52*3 = 6000，X = 5149.16；(ii) compounded continuously: X*e5.1%*3 = 6000，X = 5148.78。

2.if \$3000 is invested in a saving account that earns interest at the rate

of 5.1% compounded weekly(52 times a year) after how many fully

years will the amount at least double?

3.what annual rate compounded continuously is equivalent to an effective rate of 5.3%?

ANSWER: 假設利率為I。eI = 1.053，得到I = 5.1643%。

4.if interest is compounded continuously at an annual rate of 5.1% how

many years would it take for a principle P to triple? give your answer to

the nearest year.

ANSWER: 假設需要T年，本金會成為3倍。P * e5.1%*T = 3P，得到T = 21.54年，即22年。