Section: 计算简单利息 | 4.8 计算简单利息-interactive

Section outline

Buying a Car
::购买汽车

A red compact car parked next to greenery, highlighting a car buying lesson. — New car

When you borrow money, you have to pay it back . T his initial amount you borrowed is called the principal. Until you've paid the money back , it will collect interest (meaning that the total amount you have to repay will increase).
::当你借钱的时候,你必须偿还它。你借的这个初始金额被称为本金。在你还了钱之前,它会收取利息(这意味着你必须偿还的总额会增加 ) 。

Interest comes from a percentage of the principal. If an interest rate is 10% and the principal is $500, you would have to pay $\begin{aligned} 500 \cdot 0.10 = 50 \end{aligned}$ in interest. In total, you would owe $\begin{aligned} $ 500 + $ 50 = $ 550. \end{aligned}$
::利息来自本金的某一百分比。如果利率为10%,本金为500美元,则必须支付500元/0.10=50美元的利息。总共,你欠500元+50元=550美元。

Interest is also based on time. With simple interest , the interest rate applies to the original principal each year . This means that if you wait 3 years to pay the $500 loan back, you would be charged the $50 interest three times. After 3 years, you would owe $\begin{aligned} $ 50 + $ 50 + $ 50 = $ 150 \end{aligned}$ in interest and a total amount of $\begin{aligned} $ 500 + $ 150 = $ 650. \end{aligned}$
::利息也是按时间计算的。只要有简单的利息,利率每年适用于原始本金。这意味着,如果再等3年才能偿还500美元的贷款,你将三次收取50美元的利息。3年后,你将欠50美元+50美元=150美元的利息,总额500美元+150美元=650美元。

Use the interactive below to explore how changing the principal amount and interest rate can affect the total amount owed .
::利用以下互动方式探讨改变本金数额和利率会如何影响所欠总额。

INTERACTIVE

Buying A Car

Drag the red sliders to change the principal, the rate, or the number of years.
::拖动红色滑动符以更改本位、速率或年数。

See how these change the total interest as well as the total that is owed back.
::看看这些变化如何改变总利息和欠债总额。

Since you collect the same percent of interest on the principal each year , you can use the following formula for simple interest:
::由于您每年对本金收取相同比例的利息,您可以对简单利息使用以下公式:

\begin{aligned} Simple Interest = Principal \cdot Interest Rate \cdot Time \end{aligned}

::简单利息=本金利息利率

When using this formula, you must write the interest rate as a decimal and the time in years. You can abbreviate this as the following:
::使用此公式时,必须将利率写成小数点和年数时间。您可以缩略如下:

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

::I=PRT

Example
::示例示例示例示例

Amanda is buying a car for $16,000 and took out a loan to pay for the car. If the simple interest rate is 6% and she plans to pay it back in 5 years, how much will she pay in interest? H ow much will she owe in total for the loan?
::Amanda正在用16,000美元购买一辆汽车,并借了一笔贷款来支付汽车。如果简单的利率是6%,而且她计划在5年内还清,那么她要付多少利息?她到底欠了多少贷款?

U se the simple interest formula to solve this problem.
::使用简单的利息公式解决这个问题。

\begin{aligned} Interest = Principle \cdot Interest Rate \cdot Time \end{aligned}

::利息=利益利率原则

Interest = x
::利息=x

Principal = 16,000
::特等=16 000

Rate = 6% = 0.06
::比率=6% = 0.06

Time = 5
::时间=5

\begin{aligned} x & = 16, 000 \cdot 0.06 \cdot 5 \\ x & = 4, 800 \end{aligned}

::x=16000=0.065x=4800

Answer: The interest is $4,800 and the total amount owed for the loan is $\begin{aligned} $ 16, 000 + $ 4, 800 = $ 20, 800 \end{aligned}$ .
::答复:利息为4 800美元,贷款欠款总额为16 000美元+4 800美元=20 800美元。

Home Theater
::家居戏剧院

A modern home theater setup showcasing a large screen and control panel. — Big screen

What if a loan is paid back in less than a year or after a year and a half?
::如果贷款在不到一年或一年半后还清,怎么办?

Some stores offer loans for large purchases like televisions and cell phones. They will allow the customer to purchase the product up front but pay the store back over a relatively short period. Depending on the store, interest may be charged.
::有些商店为电视和手机等大型采购提供贷款,允许顾客提前购买产品,但在相对较短的时间内还清商店。视商店情况而定,可以收取利息。

Example
::示例示例示例示例

Jack is building a home theater which will involve buying a television for $2,000. He takes out a loan with simple interest that is to be paid back in 18 months with a yearly interest rate of 5%. How much will Jack pay in interest and how much will the television cost in total?
::Jack正在建造一所家庭剧院,其中涉及以2 000美元的价格购买一台电视机。他以简单利息贷款,18个月后还清,年利率为5%。杰克将支付多少利息,电视总成本是多少?

You must first convert months to years. Divide the number of months by 12, giving you a time of $\begin{aligned} \frac{18}{12} = \frac{3}{2} = 1 \frac{1}{2} = 1.5 \end{aligned}$ years. From here, use the simple interest formula to solve this problem.
::您必须首先转换月数到年数。将月数除以 12, 给您时间为 1812 = 32= 112= 1. 5 年。从这里, 请使用简单的利息公式解决这个问题。

\begin{aligned} Interest = Principle \cdot Interest Rate \cdot Time \end{aligned}

::利息=利益利率原则

Interest = x
::利息=x

Principal = 2,000
::特等=2 000

Rate = 5% = 0.05
::比率=5% = 0.05

Time = 1.5 years
::时间=1.5年

\begin{aligned} x & = 2, 000 \cdot 0.05 \cdot 1.5 \\ x & = 150 \end{aligned}

::x=2 000=0.05=1.5x=150

Answer: The interest is $150 and the total cost for the television is $\begin{aligned} $ 2, 000 + $ 150 = $ 2, 150 \end{aligned}$ .
::答复:利息为150美元,电视总费用为2 000美元+150美元=2 150美元。

Use the interactive below to practice writing months in terms of years using fractions and decimals.
::使用下面的交互数据,用分数和小数数来练习用年数来写几个月。

INTERACTIVE

Fraction and Decimal Practice

Calculate the number of years that is equivalent to the given number of months.
::计算相当于给定月数的年数。

Input your answers as both a mixed fraction and a decimal rounded to at least the nearest hundredth.
::以混合分数和小数小数四舍五入到至少最接近的百分百输入答案。

Check your answers with the "Check" button.
::用“ 检查” 按钮检查您的答案。

Once correct, start a new problem with the "New Number" button.
::一旦正确, 用“ 新数字” 按钮启动新问题。

Solving for a Variable
::变量的解决方案

Example
::示例示例示例示例

Jamal took out a $16,000 loan to cover the costs of starting a business. If the loan is fixed at 5% and he does not want to pay more than $1,800 in simple interest, what is the longest amount of time that Jamal can take out the loan.
::Jamal借了16 000美元的贷款来支付开办企业的费用。如果贷款固定在5%,而且他不想以简单利息支付超过1 800美元,那么Jamal能够从贷款中取出最长的贷款时间是多少。

To solve this problem, use the simple interest formula.
::要解决这个问题,请使用简单的利息公式。

\begin{aligned} Interest = Principle \cdot Interest Rate \cdot Time \end{aligned}

::利息=利益利率原则

Interest = 1,800
::利息=1 800

Principal =16,000
::特等=16 000

Rate = 5% = 0.05
::比率=5% = 0.05

Time = x
::时间=x

To find the time, you need to solve for $\begin{aligned} x . \end{aligned}$
::要找到时间, 您需要解答 x 。

\begin{aligned} 1, 800 & = 16, 000 \cdot 0.05 \cdot x \\ 1, 800 & = 800 x \\ 2.25 & = x \end{aligned}

::1 800=16 000=16 000=0.05x1 800=800x2.25=x

Answer: Jamal can take a maximum of 2.25 years to pay back the loan. You can either multiply this by 12 to get 27 months or write it as a mixed fraction , 2 ¼ years, which equals 2 years and 3 months.
::答案是:Jamal最多需要2.25年才能还清贷款。您可以乘以12来获得27个月,或者写成混合部分,2年半,相当于2年零3个月。

Introduction to Compound Interest
::复合利息入门

Modern interest is based on the idea of simple interest that emerged in 5,000 years ago Mesopotamia, but today it is much more complicated. Compound interest, for example, charges interest on the principal AND any interest earned.
::现代利息基于五千年前美索不达米亚(Mesopotamia)出现的简单利息概念,但如今却更加复杂。比如,复合利息收取本金利息和所得利息。

Use the interactive below to explore this idea.
::使用下面的交互方式来探讨这个想法。

INTERACTIVE

Introduction to Compound Interest

Learn how to calculate compound interest and amount owed step by step.
::学习如何计算复合利息和分步拖欠的金额。

Type the answers to each problem in the input box.
::在输入框中输入每个问题的答案。

ercent-of-a-number" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f45768c9244412080a859fa&collectionHandle=arithmetic&collectionCreatorID=3&conceptCollectionHandle=arithmetic-:

ercent-of-a-number&mode=lite" test-id="5f45768c9244412080a859fa">

Summary

Simple interest means the interest rate will apply to the original principal each year.
Use the formula: $\begin{aligned} simple interest = principle \times interest rate \times time \end{aligned}$ to solve simple interest problems.
::简单利率是指每年对原始本金适用利率。使用公式:简单利率=原则x利率x时间来解决简单的利息问题。

Compound interest charges interest on the principal and any interest earned.
::复利计本金利息和所得利息。

Section outline

Buying a Car ::购买汽车

Home Theater ::家居戏剧院

Solving for a Variable ::变量的解决方案

Introduction to Compound Interest ::复合利息入门

Buying a Car
::购买汽车

Home Theater
::家居戏剧院

Solving for a Variable
::变量的解决方案

Introduction to Compound Interest
::复合利息入门