Course: 5.17 解决涉及简单利益的现实世界问题

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解决涉及简单利益的现实世界问题
Nisi entered a local triathlon and won the grand prize of $4000. She decides to put all $4000 in the bank and leave it untouched for two years until she finishes high school. The bank offered her a 4% interest rate . After the two years is up, how much money will Nisi have in the bank?
::尼西进入了本地三连赛,并赢得了4000美元的大奖。她决定把所有4000美元都放入银行,在高中毕业前保留两年。银行向她提供了4%的利率。两年之后,尼西将有多少钱放入银行?

In this concept, you will learn to solve real-world problems involving simple interest.
::在这个概念中,你将学会解决现实世界中涉及简单利益的问题。

Interest
::利息利息利息利息

Saving money and making wise investments will be an important part of your financial planning. Part of investing is earning interest. When you save money in the bank, the bank uses that money for its own investments. In return for using your money, the bank pays you a certain percent. Interest is the percent that a bank pays you for keeping your money in their bank.
::储蓄和明智的投资将是你财务规划的重要组成部分。投资的一部分是赚取利息。当你在银行储蓄时,银行用这笔钱进行自己的投资。作为回报,银行用你的钱支付一定的百分之一。利息是银行用银行的钱来支付你的钱存入银行的百分之一。

All banks have an interest rate $\begin{aligned} r \end{aligned}$ which tells you what percent they will pay you per year $\begin{aligned} t \end{aligned}$ . The principal, $\begin{aligned} p \end{aligned}$ is the amount of money that you borrow or save. In order to calculate how much interest you will make, you can use the formula :
::所有银行都有利率 r , 该利率告诉你他们每年会付给你什么百分比 t。本金, p 是您借款或储蓄的金额。为了计算您将赚多少利息, 您可以使用公式 :

$\begin{aligned} I = P R T \end{aligned}$

::I=PRT

Now let’s look at an example using this formula to calculate interest.
::现在让我们看看一个使用这个公式来计算利息的例子。

You invest $5,000 in a bank for 2 years at a 3% interest rate. What is the interest you have earned after this time?
::您在银行投资 5,000 美元 2 年,利率为 3% 的利率。这次之后您赚到的利息是多少 ?

First, using the formula for simple interest, fill in all of the numbers you know.
::首先,使用简单利息的公式,填满所有你认识的数字。

$\begin{aligned} \begin{array}{rcl} p & = & $ 5000 \\ r & = & 3 % or 0.03 \\ t & = & 2 years \end{array} \end{aligned}$
::p=50000美元=3%或0.03t=2年

$\begin{aligned} \begin{array}{rcl} I & = & P R T \\ I & = & (5000) (0.03) (2) \end{array} \end{aligned}$

::I=PRTI=(5000)(0.03)(2)

Next, solve for $\begin{aligned} I \end{aligned}$ .
::下一个,解决我。

$\begin{aligned} \begin{array}{rcl} I & = & (5000) (0.03) (2) \\ I & = & 300 \end{array} \end{aligned}$

::I=50000(0.003)(2)I=300

The answer is 300.
::答案是300

You have earned $300 in interest in the two years.
::这两年你赚了三百元利息

Let’s look at another example.
::让我们再看看另一个例子。

Mrs. Payne has $20,000 to invest. She wants to earn $10,000 in interest. She is considering a savings and loans bank that is offering her 5.6% interest per year. For how long will she have to leave her money in the bank in order to reach her goal of $10,000?
::Payne夫人有20,000美元的投资。她想赚10,000美元的利息。她正在考虑一个储蓄和贷款银行,每年向她提供5.6%的利息。她需要离开银行多久才能达到10,000美元的目标?

First, using the formula for simple interest, fill in all of the numbers you know.
::首先,使用简单利息的公式,填满所有你认识的数字。

$\begin{aligned} \begin{array}{rcl} I & = & 10000 \\ p & = & $ 20000 \\ r & = & 5.6 % or 0.056 \end{array} \end{aligned}$
::I=1000p=20000r=5.6%或0.056

$\begin{aligned} \begin{array}{rcl} I & = & P R T \\ 10000 & = & (20000) (0.056) (t) \\ 10000 & = & 1120 t \end{array} \end{aligned}$

::I=PRT1000=(20000)(0.056)(t)1000=1120 t

Next, solve for $\begin{aligned} t \end{aligned}$ by dividing both sides by 1120.
::接下来,通过将双方除以1120来解决 t。

$\begin{aligned} \begin{array}{rcl} 10000 & = & 1120 t \\ \frac{10000}{1120} & = & \frac{1120 t}{1120} \\ t & = & 8.93 \end{array} \end{aligned}$

::10000120=1120 t1000120=1120 t1120t=8.93

The answer is 8.93.
::答案是8.93。

Mrs. Payne will have to leave her money in the bank for almost 9 years.
::佩恩夫人得把她的钱留在银行里将近9年了

You can use the simple interest formula $\begin{aligned} (I = P R T) \end{aligned}$ to find any of the missing variables if you are given values of the others. You have just used it to solve for $\begin{aligned} I \end{aligned}$ and $\begin{aligned} t \end{aligned}$ .
::您可以使用简单的利息公式( I=PRT) 来查找其它变量的值中缺失的变量。您只是用它来为 I 和 t 解析。

Let’s try another example.
::让我们再试一个例子。

Jessica invests $3,000 in a credit union at an interest rate of 3.9%. She leaves the money there for 5 years. What is her balance after that time?
::Jessica在信用社投资3000美元,利率为3.9%,利率为3.9%。

First, using the formula for simple interest, fill in all of the numbers you know.
::首先,使用简单利息的公式,填满所有你认识的数字。

$\begin{aligned} \begin{array}{rcl} p & = & $ 3000 \\ r & = & 3.9 % or 0.039 \\ t & = & 5 years \end{array} \end{aligned}$
::p=3,00000r=3.9%或0.039t=5年

$\begin{aligned} \begin{array}{rcl} I & = & P R T \\ I & = & (3000) (0.039) (5) \end{array} \end{aligned}$

::I=PRTI=(3,000)(0.039)(5)

Next, solve for $\begin{aligned} I \end{aligned}$ .
::下一个,解决我。

$\begin{aligned} \begin{array}{rcl} I & = & (3000) (0.039) (5) \\ I & = & 585 \end{array} \end{aligned}$

::I=3000(0.039)(5)I=585

Then, to find the bank balance, add the interest earned to the amount invested.
::然后,为了找到银行余额,将所得利息加上投资额。

$\begin{aligned} \begin{array}{rcl} balance & = & 3000 + 585 \\ = & 3585 \end{array} \end{aligned}$

::=3 000+585=3585

The answer is 3585.
::答案是3585

Jessica’s balance will be $3585 in the five years.
::Jessica的余额在五年内将达3585美元。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Nisi putting in $4000 in the bank.
::早些时候,你得到一个问题关于尼西在银行里投资4000美元。

Nisi left her $4000 prize money in the bank for two years at 4% interest. She needs to figure out how much money she now has.
::尼西把4000美元的奖金留在银行里两年,利率为4%。她需要弄清楚她现在有多少钱。

First, using the formula for simple interest, fill in all of the numbers you know.
::首先,使用简单利息的公式,填满所有你认识的数字。

$\begin{aligned} \begin{array}{rcl} p & = & $ 4000 \\ r & = & 4.0 % or 0.04 \\ t & = & 2 years \end{array} \end{aligned}$
::p=4000美元=4.0%或0.04t=2年

$\begin{aligned} \begin{array}{rcl} I & = & P R T \\ I & = & (4000) (0.09) (2) \end{array} \end{aligned}$

::I=PRTI=(40000)(0.009)(2)

Next, solve for $\begin{aligned} I \end{aligned}$ .
::下一个,解决我。

$\begin{aligned} \begin{array}{rcl} I & = & (4000) (0.04) (2) \\ I & = & 320 \end{array} \end{aligned}$

::I=(40000(0.004)(2)I=320)

Then, to find the total amount in the bank, add the interest earned to the original amount.
::然后,为了在银行中找到总金额,将所得利息加在原金额中。

$\begin{aligned} \begin{array}{rcl} balance & = & 4000 + 320 \\ = & 4320 \end{array} \end{aligned}$

::=400+320=4320

The answer is 4320. After two years, Nisi will have $4320.
::答案是4320 两年后,尼西将拥有4320美元

Example 2
::例2

A nurse put $22,000 in the bank 15 years ago. She has earned $21,450 in interest—nearly as much as her initial investment. What was the interest rate that the bank was paying her?
::15年前,一位护士在银行投注了22,000美元。她赚取了21,450美元的利息 — — 几乎和她最初的投资一样多。银行向她支付的利率是多少?

First, using the formula for simple interest, fill in all of the numbers you know.
::首先,使用简单利息的公式,填满所有你认识的数字。

$\begin{aligned} \begin{array}{rcl} I & = & $ 21450 \\ p & = & $ 22000 \\ t & = & 15 years \end{array} \end{aligned}$
::= 2 450p = 2 2000t = 15年

$\begin{aligned} \begin{array}{rcl} I & = & P R T \\ 21450 & = & (22000) (r) (15) \\ 21450 & = & 330000 r \end{array} \end{aligned}$

::I=PRT21450=(2000年)(r)(15)(15)21450=330000 r

Next, solve for $\begin{aligned} r \end{aligned}$ by dividing by 330000.
::接下来,通过除以 330000 来解决r。

$\begin{aligned} \begin{array}{rcl} 21450 & = & 330000 r \\ \frac{21450}{330000} & = & \frac{330000 r}{330000} \\ r & = & 0.065 \end{array} \end{aligned}$

::2450=330000 r21450330000=330000 r31303000=330000 r330000 r330000 r330000 r330000r=0.065

Then, multiply the value of $\begin{aligned} r \end{aligned}$ by 100 since interest rates are reported as percentages.
::然后,将r值乘以100,因为利率作为百分比报告。

$\begin{aligned} \begin{array}{rcl} r & = & 0.065 \times 100 \\ r & = & 65 % \end{array} \end{aligned}$

::r=0.065x100r=65%

The answer is 6.5%.
::答案是6.5%。

The nurse invested at 6.5% interest.
::护士投资6.5%的利息。

Example 3
::例3

An investor places $15,000 in a savings account that pays 4.5% interest. She will leave the money there for 6 years. What will her interest be?
::投资者将15,000美元存入一个支付4.5%利息的储蓄账户。她将把这笔钱留在那里6年。她的利息是多少?

First, using the formula for simple interest, fill in all of the numbers you know.
::首先,使用简单利息的公式,填满所有你认识的数字。

$\begin{aligned} \begin{array}{rcl} p & = & $ 15000 \\ r & = & 4.5 % or 0.045 \\ t & = & 6 years \end{array} \end{aligned}$
::p=15 000美元=4.5%或0.045t=6年

$\begin{aligned} \begin{array}{rcl} I & = & P R T \\ I & = & (15000) (0.045) (6) \end{array} \end{aligned}$

::I=PRTI=(1500)(0.045)(6)

Next, solve for $\begin{aligned} I \end{aligned}$ .
::下一个,解决我。

$\begin{aligned} \begin{array}{rcl} I & = & (15000) (0.045) (6) \\ I & = & 4050 \end{array} \end{aligned}$

::I=1500(0.045)(6)I=4050

The answer is 4050.
::答案是4050

The investor earned $4050 in interest in the six years.
::投资者在这六年中赚取了4050美元的利息。

Example 4
::例4

A bank is offering an interest rate of 4.75%. How long would it take to earn $500 if you invested $12,000 in the bank?
::银行提供4.75%的利率。在银行投资12 000美元需要多久才能赚到500美元?

First, using the formula for simple interest, fill in all of the numbers you know.
::首先,使用简单利息的公式,填满所有你认识的数字。

$\begin{aligned} \begin{array}{rcl} I & = & $ 500 \\ p & = & $ 12000 \\ r & = & 4.75 % or 0.0475 \end{array} \end{aligned}$
::I=500美元=1,200美元=4.75%或0.0475美元

$\begin{aligned} \begin{array}{rcl} I & = & P R T \\ 500 & = & (12000) (0.0475) (t) \\ 500 & = & 570 t \end{array} \end{aligned}$

::I=PRT500=(2000年)(0.0475)(t)500=570吨

Next, solve for $\begin{aligned} t \end{aligned}$ by dividing both sides by 570.
::接下来,通过将双方除以570来解决 t。

$\begin{aligned} \begin{array}{rcl} 500 & = & 570 t \\ \frac{500}{570} & = & \frac{570 t}{570} \\ t & = & 0.877 \end{array} \end{aligned}$

::500=570t50057070=570t570t570t=0.877

The answer is 0.88.
::答案是0.88。

It would take 0.88 years or 10.6 months to gain $500 in interest.
::需要0.88年或10.6个月才能获得500美元的利息。

Example 5
::例5

If you charge $7,000 on a credit card and you bank charges you 15.9%, how much would you owe after a year?
::如果你用信用卡收7000美元银行收你15.9%,一年后还欠你多少钱?

First, using the formula for simple interest, fill in all of the numbers you know.
::首先,使用简单利息的公式,填满所有你认识的数字。

$\begin{aligned} \begin{array}{rcl} p & = & $ 7000 \\ r & = & 15.9 % or 0.159 \\ t & = & 1 year \end{array} \end{aligned}$
::p=7000美元=15.9%或0.159t=1年

$\begin{aligned} \begin{array}{rcl} I & = & P R T \\ I & = & (7000) (0.159) (1) \end{array} \end{aligned}$

::I=PRTI=(700) (0.159)(1)

Next, solve for $\begin{aligned} I \end{aligned}$ .
::下一个,解决我。

$\begin{aligned} \begin{array}{rcl} I & = & (7000) (0.159) (1) \\ I & = & 1113 \end{array} \end{aligned}$

::I=70000(0.159)(1)I=1113

Then, to find the total owing after one year, add the interest earned to the amount borrowed.
::然后,为了找到一年后拖欠的总额,在借款额中加上利息收入。

$\begin{aligned} \begin{array}{rcl} amount owing & = & 7000 + 1113 \\ = & 8113 \end{array} \end{aligned}$

::应付款项=7000+1113=8113

The answer is 8113.
::答案是8113

You would owe $8113 after one year.
::一年后你欠我八百一十三元

Review
::回顾

Use the simple interest formula $\begin{aligned} I = P R T \end{aligned}$ to solve for the Interest.
::使用简单的利息公式 I= PRT 来解决利息问题。

1. Find $\begin{aligned} I \end{aligned}$ if $\begin{aligned} p = 62, 300, r = 0.0525, t = 14 \end{aligned}$ .
::1. 查找p=62 300,r=0.0525,t=14。

2. Find $\begin{aligned} I \end{aligned}$ if $\begin{aligned} p = 9800, r = 0.028, t = 9 \end{aligned}$ .
::2. 发现我是否p=9800,r=0.028,t=9。

3. Find $\begin{aligned} I \end{aligned}$ if $\begin{aligned} p = $ 600, r = 0.05, t = 8 \end{aligned}$
::3. 发现p=600美元,r=0.05,t=8

4. Find $\begin{aligned} I \end{aligned}$ if $\begin{aligned} p = $ 2300, r = 0.06, t = 12 \end{aligned}$
::4. 发现p=2300,r=0.06,t=12

5. Find $\begin{aligned} I \end{aligned}$ if $\begin{aligned} p = $ 5500, r = 0.08, t = 7 \end{aligned}$
::5. 如果p=5500美元,r=0.08,t=7,请查I=5500,r=0.08,t=7

6. Find $\begin{aligned} I \end{aligned}$ if $\begin{aligned} p = $ 400, r = 0.05 \end{aligned}$ , $\begin{aligned} t = 57 \end{aligned}$ .
::6. 发现p=400美元,r=0.05,t=57。

7. Find $\begin{aligned} I \end{aligned}$ if $\begin{aligned} p = $ 700, r = 0.03 \end{aligned}$ , $\begin{aligned} t = 9 \end{aligned}$
::7. 如果p=700,r=0.03,t=9,请查I=700,r=0.03,t=9

8. Find $\begin{aligned} I \end{aligned}$ if $\begin{aligned} p = $ 500, r = 0.06 \end{aligned}$ , $\begin{aligned} t = 12 \end{aligned}$
::8. 如果p=500美元,r=0.06,t=12,则查找I

9. Find $\begin{aligned} I \end{aligned}$ if $\begin{aligned} p = $ 800, r = 0.09 \end{aligned}$ , $\begin{aligned} t = 7 \end{aligned}$
::9. 查找p=800美元,r=0.09,t=7的p=800,r=0.09,t=7

10. Find $\begin{aligned} I \end{aligned}$ if $\begin{aligned} p = $ 950, r = 0.06 \end{aligned}$ , $\begin{aligned} t = 4 \end{aligned}$
::10. 发现p=950美元,r=0.06,t=4

Find the interest to calculate the new balance with the given information. There are two steps to solving these problems.
::根据给定的信息找到计算新平衡的利息。解决这些问题有两个步骤。

11. $\begin{aligned} p = 43000, r = 0.0365, t = 11 \end{aligned}$
::11p=43,000,r=0.0365,t=11

12. $\begin{aligned} p = 7000, r = 0.079, t = 4 \end{aligned}$
::12p=700,r=0.079,t=4

13. $\begin{aligned} p = 8000, r = 0.06, t = 3 \end{aligned}$
::13p=8,000,r=0.06, t=3

14. $\begin{aligned} p = 18000, r = 0.04, t = 5 \end{aligned}$
::14p=18000,r=0.04, t=5

15. $\begin{aligned} p = 25000, r = 0.05, t = 3 \end{aligned}$
::15p=2500,r=0.05,t=3

16. $\begin{aligned} p = 3000, r = 0.05, t = 7 \end{aligned}$
::16p=3000,r=0.05,t=7

17. $\begin{aligned} p = 12000, r = 0.04, t = 5 \end{aligned}$
::17p=12000,r=0.04,t=5

18. $\begin{aligned} p = 9000, r = 0.06, t = 10 \end{aligned}$
::18 p=900,r=0.06, t=10

19. $\begin{aligned} p = 7500, r = 0.03, t = 8 \end{aligned}$
::19p=7500,r=0.03, t=8

20. $\begin{aligned} p = 27500, r = 0.04, t = 6 \end{aligned}$
::20.p=27500,r=0.04,t=6

Review (Answers)
::回顾(答复)

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。

Resources
::资源

Section outline

General

解决涉及简单利益的现实世界问题

Interest ::利息利息利息利息

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Interest
::利息利息利息利息

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源