1971 AMC 12 第 4 题

Question

按年利率

5\%

计入两个月的单利后，某童子军团在理事会金库中的总额为

\$255.31

。所计利息为若干美元再加上下列多少美分：

After simple interest for two months at

5\%

per annum was credited, a Boy Scout Troop had a total of

\$255.31

in the Council Treasury. The interest credited was a number of dollars plus the following number of cents:

11

12

13

21

31

两个月是一年的六分之一

Two months is one-sixth of a year

若

P

是本金，解方程

255.31=P(1+\frac{0.05}{6})

If

P

is the principal, solve

255.31=P(1+\frac{0.05}{6})

若

P

是本金，则

\begin{aligned} 255.31&=P\left(1+\frac{0.05}{6}\right)\\ &=P\frac{121}{120}\text{。} \end{aligned}

因此

P=253.20

，利息为

\$2.11

，其中的美分数为

11

。

因此，正确答案为 A。

If

P

is the principal, then

\begin{aligned} 255.31&=P\left(1+\frac{0.05}{6}\right)\\ &=P\frac{121}{120}. \end{aligned}

Hence

P=253.20,

so the interest is

\$2.11

and its cents part is

11.

Therefore, the correct answer is A.

其他年份的第 4 题