6.20简单的利率方程求利率

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  简单的利率方程求利率

  

  [Figure 1]

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  The  loan  statement for Margot’s family’s car arrived in the mail. Margot noticed that the amount due was $175.67 if paid by October 25. However, the loan originator noted that if payment arrived after this date the amount due would be $186.21. What simple interest  rate  does the loan originator charge on the loan if it is late?
  ::Margot注意到,如果在10月25日之前支付,到期金额为175.67美元。 然而,贷款发起人指出,如果在这一日期之后支付,到期金额将是186.21美元。 如果贷款发起人迟到,贷款的发起人收取什么简单的利率?

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  In this concept, you will learn to use the simple interest  equation  to find an interest rate.
  ::在此概念中,您将学会使用简单的利息方程式来寻找利率。

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  Using the Simple Interest Equation to Find Interest Rates
  ::使用简单利率等量来查找利率

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  Interest  is a charge for money that is borrowed. When you borrow money, you pay the lender interest for the privilege of borrowing the money. On the flipside, when you deposit money into a saving account at a bank, the bank pays you interest since the bank is borrowing money from you. So interest can be something either that you have to pay or that is paid to you.
  ::利息是借钱的利息。 当你借钱时,你为借钱的特权而向放款人支付利息。 在反面,当你把钱存入银行的储蓄账户时,银行支付利息,因为银行正在向你借款。所以利息可以是必须支付的东西,也可以是付给你的东西。

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  The amount of money that is invested or borrowed is called the  principal . If you borrow $500, this is the principal. It is the initial amount before any interest is added on.
  ::投资或借入的金额称为本金。如果借入500美元,这是本金。先是初始金额,再加利息。

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  The  rate of interest  is the percent charged or earned. You also have to consider the time in years that the money is borrowed or deposited when computing interest.
  ::利率是收取或赚取的百分率。您还必须考虑到在计算利息时借出或存入钱的年份中的时间 。

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  You can calculate interest by using this equation:
  ::您可以使用此方程式计算利息 :

  $$\begin{array}{r}\begin{array}{rcl}\text{Interest}& =& \text{Principal}\times \text{rate}\times \text{time}\\ I& =& Prt\end{array}\end{array}$$

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  If you know the amount of interest, the principal, and the time in years, you can find the interest rate.
  Let’s look at an example.
  ::如果您知道利息金额、本金和年中的时间,您可以找到利率。让我们来举个例子。

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  If you deposit $2,000 at USA Savings Bank, at the end of two years you will have received $240 in simple interest. What is the interest rate at USA Savings Bank?
  ::如果你在美国储蓄银行存款2 000美元,在两年结束时,你将获得240美元的简单利息。 美国储蓄银行的利率是多少?

  $$\begin{array}{r}\begin{array}{rcl}I& =& Prt\\ \$240& =& \$2,000\times r\times 2\leftarrow \text{Substitute values}.\\ \$240& =& \$4,000\times r\leftarrow \text{Simplify}.\\ 0.06& =& r\leftarrow \text{Solve for}r.\end{array}\end{array}$$

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  Change 0.06 to the percent 6%.
  ::将0.06%改为0.06%。

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  The answer is the interest rate is 6%.
  ::答案是利率是6%。

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  Let’s take a look at another example.
  ::让我们看看另一个例子。

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  If you borrow $3,600 from USA Savings Bank for 18 months, at the end of the 18 months you will repay $4,059 to the bank. What is the interest rate for this loan?
  ::如果你向美国储蓄银行借款3 600美元,为期18个月,在18个月结束时,你将向银行偿还4 059美元。这笔贷款的利率是多少?

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  First, note that the amount to be repaid includes the principal plus the interest.
  ::第一,注意应偿还的数额包括本金加利息。

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  Next, subtract the principal from the amount to be repaid to find the amount of the interest.
  ::其次,从应偿还的金额中减去本金,以找到利息数额。

  $$\begin{array}{r}\$4,059-\$3,600=\$459\end{array}$$

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  Then, since there are 12 months in a year, 18 months is  $\begin{array}{r}18÷12\end{array}$  or  $\begin{array}{r}1\frac{1}{2}\end{array}$ .
  ::然后,因为一年有12个月, 18个月是18,12或12。

  $$\begin{array}{r}\begin{array}{rcl}I& =& Prt\\ \$459& =& \$3,600\times r\times 1\frac{1}{2}\leftarrow \text{Substitute values}.\\ \$459& =& \$5,400\times r\leftarrow \text{Simplify}.\\ 0.085& =& r\leftarrow \text{Solve for}r.\end{array}\end{array}$$

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  Finally, change 0.085 to the percent 8.5%
  ::最后,将0.085改为8.5%

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  The answer is the interest rate is 8.5%.
  ::答案是利率为8.5%。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Margot’s family’s car loan statement.
  ::更早之前, Margot 一家的汽车贷款声明给您带来了一个问题。

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  The loan originator charges interest if the loan is not paid by a certain date. If paid by October 25, the amount owed is $175.67. If paid after this date the amount owed is $186.21. What simple interest rate does the loan originator charge on the loan if it is late?
  ::如果贷款未在某一日期偿还,贷款发起人收取利息。如果在10月25日之前偿还,则欠款为175.67美元。如果在此日期之后偿还,则欠款为186.21美元。贷款发起人对贷款收取什么简单的利率,如果贷款迟到呢?

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  First, change 1 month to years:  $\begin{array}{r}\frac{1}{12}=0.0833\end{array}$
  ::第一,将一个月改为一年:1 12 = 0.0833

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  Next, find the interest that will be owed by subtracting:  $\begin{array}{r}\$186.21-\$175.67=\$10.54\end{array}$
  ::其次,找出减去186.21美元-175.67美元=10.54美元后所欠利息。

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  Then, plug the values into the equation.
  ::然后,在方程中插入值。

  $$\begin{array}{r}\begin{array}{rcl}I& =& Prt\\ \$10.54& =& \$175.67\times r\times 0.0833\leftarrow \text{Substitute values}.\\ \$10.54& =& \$14.63\times r\leftarrow \text{Simplify}.\\ 0.7204& =& r\leftarrow \text{Solve for}r.\end{array}\end{array}$$

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  Finally, change 0.7204 to the percent 72.04%.
  ::最后,将0.7204改为72.04%。

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  The answer is the interest rate is 72.04%.
  ::答案是利率是72.04%。

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  Example 2
  ::例2

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  Wanda borrowed $5,000.00 from the bank. At the end of three years, she had paid $450.00 in interest. What is Wanda’s interest rate?
  ::Wanda向银行借款5 000.00美元。在三年结束时,她支付了450.00美元的利息。 Wanda的利率是多少?

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  To figure this out, you can use the  formula  for finding simple interest.
  ::要弄清楚这一点,你可以使用公式来寻找简单的利息。

  $$\begin{array}{r}I=Prt\end{array}$$

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  First, fill in what you know.
  ::首先,填上你知道的

  $$\begin{array}{r}450=5,000\times r\times 3\end{array}$$

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  Next, you are trying to figure out the rate, so that is your  variable .  $\begin{array}{r}450=15,000r\end{array}$
  ::接下来,你试图找出费率, 这就是你的变量。 450=15,000 r。

  $$\begin{array}{r}\frac{450}{15,000}=0.03\text{or}3\mathrm{\%}\end{array}$$

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  The answer is Wanda’s interest rate is 3%.
  ::答案是万达的利率为3%。

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  Example 3
  ::例3

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  Jesse borrowed $500.00. At the end of the year he paid back $50.00 in interest. What was the interest rate?
  ::杰西借了500美元,年底他还还了50美元利息,利率是多少?

  $$\begin{array}{r}\begin{array}{rcl}I& =& Prt\\ \$50& =& \$500\times r\times 1\leftarrow \text{Substitute values}.\\ \$50& =& \$500\times r\leftarrow \text{Simplify}.\\ \$0.10& =& r\leftarrow \text{Solve for}r.\end{array}\end{array}$$

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  Change 0.10 to the percent 10%.
  ::将0.10%改为10%。

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  The answer is the interest rate is 10%.
  ::答案是利率是10%

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  Example 4
  ::例4

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  Karen earned $200.00 in two years of simple interest on her initial investment of $400.00. What was the interest rate?
  ::Karen最初投资400.00美元,在两年的简单利息中挣了200.00美元。 利率是多少?

  $$\begin{array}{r}\begin{array}{rcl}I& =& Prt\\ \$200& =& \$400\times r\times 2\leftarrow \text{Substitute values}.\\ \$200& =& \$800\times r\leftarrow \text{Simplify}.\\ 0.25& =& r\leftarrow \text{Solve for}r.\end{array}\end{array}$$

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  Change 0.25 to the percent 25%.
  ::将0.25%改为25%。

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  The answer is the interest rate is 25%.
  ::答案是利率是25%

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  Example 5
  ::例5

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  Principal: $5,600; Time: 9 months; Simple interest: $357
  ::特等:5 600美元;时间:9个月;简单利息:357美元

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  First, change 9 months to years:  $\begin{array}{r}\frac{9}{12}=\frac{3}{4}=0.75\end{array}$
  ::第一,将9个月改为9年:9 12 = 3 4 = 0.75

  $$\begin{array}{r}\begin{array}{rcl}I& =& Prt\\ \$357& =& \$5,600\times r\times 0.75\leftarrow \text{Substitute values}.\\ \$357& =& \$4,200\times r\leftarrow \text{Simplify}.\\ 0.085& =& r\leftarrow \text{Solve for}r.\end{array}\end{array}$$

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  Change 0.085 to the percent 8.5%.
  ::将0.085改为8.5%。

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  The answer is the interest rate is 8.5%.
  ::答案是利率为8.5%。

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  Review
  ::回顾

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  Find the simple interest on each amount.
  ::找出每个金额的简单利息。

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  1. $500.00 at 4% for 2 years
     ::两年,500.00美元,按4%计算
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  2. $200.00 at 5% for 3 years
     ::3年200.00美元,按5%计算,为期3年
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  3. $5,000.00 at 2% for 2 years
     ::5 000.00美元,按2%计算,两年为2%
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  4. $600.00 at 10% for 1 year
     ::600.00美元,按1年10%的10%计算
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  5. $1,200.00 at 4% for 2 years
     ::1 200.00美元,按2年4%的4%计算
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  6. $1,500.00 at 3% for 1 year
     ::1年1美元1 500美元,按3%的3%计算
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  7. $2,300.00 at 2% for 2 years
     ::2年按2%计算,2年按2%计算,2 300.00美元
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  8. $500.00 at 4% for 2 years
     ::两年,500.00美元,按4%计算
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  9. $2,500.00 at 5% for 5 years
     ::5年2 500美元,按5%5%计算
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  10. $1,500.00 at 11% for 2 years
      ::1,500美元,按11%计算,两年1年1,500美元
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  11. $3,500 at 3% for 5 years
      ::5年3 500美元,3%,3年3 500美元
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  12. $3,500 at 4% for 15 years
      ::15年3 500美元,按4%的4%计算
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  13. $13,000 at 4.5% for 6 years
      ::6年13,000美元,按4.5%的4.5%计算
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  14. $23,000 at 3.5% for 10 years
      ::10年,23 000美元,3.5%,为期10年
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  15. $50,000 at 2.5% for 20 years
      ::20年50 000美元,按2.5%计算,20年

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  Review (Answers)
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源

   

  
  

  
  
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