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金融术语解析02-APR and EAR - 知乎

金融术语解析02-APR and EAR - 知乎切换模式写文章登录/注册金融术语解析02-APR and EAR经融学人忠与理想，面对现实废话不多说☟年利率（Annual Percentage Rate，APR）：就是单利，比如银行说存（贷）款利率10%，你准备存（贷）100，那么一年后本息为110.有效年利率（Effective Annual Rate，EAR）：按照给定的计息期利率和每年复利次数计算利息时，能够产生相同结果的每年复利一次的年利率。翻译过来就是复利，有些银行的金融产品计息周期是小于一年的，比如你在年初存（贷）100元，APR10%，半年结一次息，那么6月本息为105，12月本息为110.25，实际利率大于10%，因为从第二期计算时不但计算了本金的利息，还计算了累计利息的利息。当计息的复利周期小于一年时，EAR会大于APR，等于一年时，EAR=APR。以季度为例，季度6%的利率对应只复利一次的时的年利率为6.13636EAR的计算公式（m为复利次数） 那么问题来了，EAR有什么鸟用？平时哥去Bank存钱借钱到底用的是APR还是EAR？银行用的利率都是EAR。但要注意，分期还款时的坑：下面有请A爷、B哥A:B哥，最近手头紧，借个1W来花花B：握草，你以为我开银行的吗，要借可以，12%利息，现在银行利息都15%，我便宜你了A:好哥们！年底我还1200给你对吧B：NO,no, 我要分期还款，我每个月会微信给你账单A：那也行！(银行卡设置自动还款,高级！）一年过去，还是单身。。。A看账单，傻眼了1月 1202月 1223月 126。。。。。一大推数字正在袭来A:喂喂，B哥，你给我解释解释，啥意思！B：什么啥意思！哥把钱借你，也有机会成本啊，不说了吗，银行利率15%，我干嘛不存银行，还不是看着你是我好兄弟的面子上？所以我对每个月的利息只收12%的利息，便宜你了A:额（点头），谢谢啊（内心独白：妈的，高中数学课不该睡觉的，赶紧上知乎看看）B内心独白：哈哈，真好忽悠，这样复利12次后真实EAR利率都有20%，老子赚大了！编辑于 2020-07-25 13:05利息贷款利息利率​赞同 55​​8 条评论​分享​喜欢​收藏​申请

信贷业务中的利率介绍（ APR 和 IRR ） - 知乎

信贷业务中的利率介绍（ APR 和 IRR ） - 知乎首发于数据化风控切换模式写文章登录/注册信贷业务中的利率介绍（ APR 和 IRR ）过一点画一条直线业务背景随着社会的发展，提前消费的观念越来越被年轻一代所接受，我们的生活也开始和各种信贷产品产生了交集。对于有信贷需求的人来说最关注的就是额度和利率，额度基本是基于申请人的收入水平来计算，而利率则和用户质量以及机构风控水平息息相关。在常见的信贷产品介绍中（某呗、信用卡分期、房贷、平台借贷、消费分期、消费贷等）都有关于还款方式和利率的说明，例如对于还款方式则有：随借随还、先息后本、等本等息、等额本金、等额本息等，对于利率则有：日利率万3、月利率0.75%、年化利率12%等。很多人在选择不同产品的时候通常是将产品说明中介绍的利率乘以相应的天数折算成年化利率进行对比（日利率365，月利率12），从而选择年化利率低的产品。如果采用这种方法来选择信贷产品则很可能让我们进入圈套，选择了高利率的产品而不自知，利率看似简单，实则还真不简单。本文将结合信贷产品的还款方式来介绍年化利率 ( Annual Percentage Rate, APR ) 和内部收益率 ( Internal Rate of Return, IRR ) 。APR 就是常说的名义利率，IRR 就是常说的真实利率。目录 Part 1. 还款方式 Part 2. APR 和 IRR Part 3. 总结 版权声明 参考资料 Part 1. 还款方式在介绍利率之前我们先来介绍几个常见的还款方式，主要包括：随借随还、先息后本、等本等息、等额本金、等额本息。1. 随借随还随借随还是指客户在获得授信额度后可以随时来支取，借出后就开始计算利息；借出后可以随时还款，还款后额度会进行恢复，一般用于银行的大额消费贷、借呗等。随借随还的贷款计算公式如下：总还款利息 = 贷款本金 * 日利率 * 贷款天数下面举个例子进行说明：随借随还：借款12000，借款期限12个月，月利率（ 10% / 12 ） 总还利息 = 12000 * ( 10% / 365 ) * 365 = 1200 2. 先息后本先息后本是指每月支付利息，到期后归还本金，这种还款方式更适合现金流压力较大，而一定时间后才会有一笔钱进账的个人或企业使用。先息后本的计算公式如下：每月还款利息 = 贷款本金 * 月利率总还款利率 = 贷款本金 * 月利率 * 还款月数下面举个例子进行说明：先息后本：借款12000，借款期限12个月，月利率（ 10% / 12 ）每个月应还利息 = 12000 * 10% / 12 = 100 总还利息 = 12000 * 10% = 1200 3. 等本等息等本等息是指每个月偿还的本金相等，利息也相等，一般用于银行卡现金分期或者账单分期。等本等息的贷款计算公式如下：每月还款本息 = （贷款本金 / 还款月数）+ 贷款本金 * 月利率总还款利息 = 贷款本金 * 月利率 * 还款月数下面举个例子进行说明：等本等息：借款12000，借款期限12个月，月利率（ 10% / 12 ）每个月应还本金 = 12000 / 12 = 1000 每个月应还利息 = 12000 * 10% / 12 = 100 每个月应还本息 = 1000 + 100 = 1100 总还利息 = 12000 * 10% = 12004. 等额本金等额本金是指在贷款期内每月偿还同等数额的本金和剩余贷款在该月所产生的利息。其特点就是，每期所还本金相等，利息逐月减少（根据剩余未还本金计算），总还款额逐月递减。等额本金是住房贷款的两种常见还款方式之一，其贷款计算公式如下：每月还款本息 = （贷款本金 / 还款月数）+ （贷款本金 - 已归还本金） * 月利率总还款利息 = 贷款本金 * 月利率 * （还款月数 + 1）/ 2下面举个例子进行说明：等额本金：借款12000，借款期限12个月，月利率（ 10% / 12 ）每个月应还本金 = 12000 / 12 = 1000 第1个月应还利息 = 12000 * 10% / 12 = 100 第2个月应还利息 = ( 12000 - 1000 ) * 10% / 12 = 91.67 ... 第N个月应还利息 = ( 12000 - 1000 * ( N-1 ) ) * 10% / 12 ... 第12个月应还利息 = ( 12000 - 1000 * 11 ) * 10% / 12 = 8.33 总还利息 = 12000 * 10% / 12 * ( 12 + 1 ) / 2 = 6505. 等额本息等额本息是指在贷款期内每月按相等的金额偿还贷款本息，其中利息逐月递减，本金逐月递增。其特点就是，由于每月的还款额相等，因此，在贷款初期每月的还款中，剔除按月结清的利息后，所还的贷款本金就较少；在贷款末期每月的还款中，剔除按月结清的利息后，所还的贷款本金就较多。等额本息是住房贷款的两种常见还款方式之一，其贷款计算公式如下：每月还款本息 = \frac{贷款本金月利率(1+月利率)^{还款月数}}{(1+月利率)^{还款月数}-1} 第m期剩余应还本金 = 贷款本金(1+月利率)^m - \frac{每月还款本息[(1+月利率)^{还款月数}-1]}{月利率} 总还款利息 = 每月还款本息 * 还款月数 - 贷款本金 下面举个例子进行说明：等额本息：借款12000，借款期限12个月，月利率（ 10% / 12 ）每个月应还本息 = 1055 第1个月还款利息 = 12000 * 10% / 12 = 100 第1个月还款本金 = 1055 - 100 = 955... 第12个月还款利息 = 9 第12个月还款本金 = 1046 总还利息 = 1055 * 12 - 12000 = 660 6. 小结看完上面 这些还款方式的介绍我们来做个小结，看看相同的贷款本金和利率下，不同方式的总还利息之间的差别：随借随还：应还利息 1200 先息后本：应还利息 1200 等本等息：应还利息 1200 等额本金：应还利息 650 等额本息：应还利息 660从应还利息上来看，等额本金和等额本息的还款方式所还利息最少，随借随还、先息后本、等本等息还款方式所还利息相同，同样标着月利率（ 10% / 12 ），怎么不同还款方式所还利息差别这么多。从所还利息角度来看，这是不是说明等额本金的利息最低，随借随还、先息后本和等本等息的还款方式利息最高？想要弄清楚这个问题，就要先了解名义利率APR和实际利率IRR之间的差别，且继续往下看 。Part 2. APR 和 IRR聊完了还款方式，有没有觉得不同的还款方式差别很大，下面我们再来谈谈利率。1. 名义利率APR APR，即年化利率，又称名义利率,是指一年内对贷款计息时，对外给出的年利率，年利率 = 息费之和 / 借款本金。针对上面 Part 1里介绍的各种还款方式，他们的名义利率APR如下：图1. 各还款方式下的名义利率2. 真实利率IRRIRR，即内部收益率，也称为真实利率，是指借款现值总金额与偿还本息现值总金额相等时，净现值（Net Present Value, NPV）等于0时的折现率。由于货币有时间价值，后期获得的回报需要用一定的利率折现，这样不同时间点的收益全部折现到当前时间点，再做一个总和，即“净现值”。IRR是和NPV紧密相连的，其计算公式过于复杂，这些就不具体介绍了，感兴趣的同学可以参考知乎圆桌关于IRR的讨论：简单的讲，作为投资方，投资出去一笔钱之后，赚取的回报现金流入时间点和流入金额大小会影响IRR的大小。下面举个例子进行说明：小明借给张三10000块钱，约定年化利率10%，本息共计11000，1年内还清。还款方式有两种：第一种是每6个月还5500，分两次还清；第二种是1年后一次性还清11000。针对这两种方法，我想大家都会选择方案1，一个简单的逻辑就是先拿回来的5500元还可以拿去投资半年获得收益，从而整体收益会高于方案2。从实际计算IRR上来看，方案1也会高于方案2。从宏观角度来看，IRR 最通俗的理解为项目投资收益能承受的货币贬值，通货膨胀的能力。比如内部收益率 10%，表示该项目操作过程中每年能承受货币最大贬值 10%，或通货膨胀 10%。当我们需要计算 IRR 时，可以使用 Excel 中的 IRR 函数，我们以Part 1中先息后本的方案为例进行说明，具体流程和计算方式如下：1. 模拟现金流：第0个月流出现金流 12000，第1个月流入现金流 100，第二个月流入现金流 100, ... , 第12个月流入现金流 12100。2. 使用IRR函数进行计算获得实际每期利率，在这里也就是实际月利率3. 实际月利率 * 12 即可得到真实利率IRR 按这个方法，我们分别计算下 Part 1 中介绍的五种还款方式所对应的IRR，如下图所示：图2. 不同还款方式的IRR和APR从 APR 角度来看，同样是名义利率 APR 为 10% 的随借随还、先息后本、等本等息三种还款方式，随借随还和先息后本的真实利率 IRR 相差不大，且先息后本的IRR=APR，但是等本等息的IRR和APR相差巨大。虽然这三种还款方式应还本息相同，但是真实利率 IRR 相差较大。从 IRR 角度来看，等额本金、等额本息和先息后本的真实利率IRR都为10%，但是等额本金和等额本息的名义利率APR明显更低。3. 等额本金和等额本息的讨论对比等额本金和等额本息两种还款方式，它们IRR相等，但是等额本金的APR更低，那是不是说明等额本金更节省利息呢？其实并不是那么回事。贷款利息的多少由什么因素决定大家都知道，钱在银行存一天就有一天的利息，存的钱越多，得到的利息就越多。同样，对于贷款来说也一样，银行的贷款多用一天，就要多付一天的利息，贷款的金额越大，支付给银行的利息也就越多。银行利息的计算公式是：利息 = 资金额 × 利率 × 占用时间因此，利息的多少，在利率不变的情况下，决定因素只能是资金的实际占用时间和占用金额的大小，而不是采用哪种还款方式。利息随资金实际占用数量及期限长短的变化而增减。从 Part 1 的介绍中我们可以知道，等额本金的还款方式是每月还固定本金，而等额本息的还款方式是每月还固定的本息（前期所还利息多，本金少，随着时间的推移，所还本机增加，利息减少）。在还款的早期，采用等额本金的方式能使贷款剩余本金减少的比等额本息的方式更快，因此所还利息较少。换句话说，造成等额本息还款利息多的原因是该方式在同期持有的贷款本金更多，因此利息也会更多。不管采取等额本金还是等额本息的贷款还款方式，银行都没有做吃亏的买卖，客户也不存在节省利息支出的实惠。Part 3. 总结在实际产品利率的宣传过程中，针对采用等额本息、等额本金作为还款方式的房贷，宣传的利率往往是较高的真实利率 IRR，而对于一些采用等本等息作为还款方式的消费分期产品，宣传的利率往往是更低的年化利率 APR，大都报低实高，因此在选择信贷产品的时候，一定要仔细计算真实利率 IRR，以免上当受骗。版权声明欢迎转载分享，请在文章中注明作者和原文链接，商业转载请联系作者获得授权，非商业转载请注明出处。原文作者：过一点画一条直线（知乎ID） 知乎专栏：数据化风控 原文链接：https://zhuanlan.zhihu.com/p/161405128参考资料关于作者：本人就职于某科技公司从事风控算法策略、数据挖掘相关工作，欢迎互相交流，共同成长。编辑于 2020-09-24 09:12互联网金融风险管理金融常识​赞同 406​​57 条评论​分享​喜欢​收藏​申请转载​文章被以下专栏收录数据化风控风控理论与实践菜鸟变形记

【月份縮寫】Jan, Mar, Apr, Jun 等是幾月？ – 英文庫

【月份縮寫】Jan, Mar, Apr, Jun 等是幾月？ – 英文庫

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【月份縮寫】Jan, Mar, Apr, Jun 等是幾月？

Hello, everyone! 我是英文庫的 Celine ，今天來看看各月份的英文縮寫是什麼～

在年曆或一些文件上，常會看到月份的縮寫，而在撰寫電子郵件或安排時間時，也會需要用到月份的英文縮寫，以方便溝通。

基本上，月份的英文縮寫就是取前三個字母，再加上縮寫點，除了五月的 May 本來就只有三個字母，所以不會再加縮寫點。

月份

各月份的英文

各月份的英文縮寫

一月

January

Jan.

二月

February

Feb.

三月

March

Mar.

四月

April

Apr.

五月

May

May

六月

June

Jun.

七月

July

Jul.

八月

August

Aug.

九月

September

Sep. / Sept.

十月

October

Oct.

十一月

November

Nov.

十二月

December

Dec.

小提醒：

縮寫點並非必要的，但記得第一個字母一定要大寫，而全部大寫的寫法也是滿常見的。以一月為例，Jan. / Jan / JAN 這三種寫法都是可以的唷！

九月 September 有兩種縮寫寫法，外國人比較常使用 Sept.，但如果是要與其他月份縮寫一致時就會使用 Sep.。

如果是正式的文件或文章就盡量不要使用縮寫喔！

如果想知道更多細節與相關用法，可以參考以下文章：

日期/月份/星期/時間 正確英文格式、寫法！一次搞懂！

該用 In, On, 還是 At? 來搞懂「時間介系詞」

未來如果遇到任何英文疑問時，要記得回來英文庫找答案喔！

Celine

Hello! ：）

是一個心思細膩、喜歡嘗試不同事物的英文老師，覺得英文可以讓你的世界更廣大，希望能幫助你學英文，讓生命更美好！❤️

歡迎來到英文庫！我們每天為你創造最實用的教學文章！若想支持我們，可以看看我們的四個產品：

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低利时代，人人都要清楚APR与IRR的差别到底有多大 - 知乎

低利时代，人人都要清楚APR与IRR的差别到底有多大 - 知乎首发于来FAL学风险控制切换模式写文章登录/注册低利时代，人人都要清楚APR与IRR的差别到底有多大FAL金科应用研究院​已认证账号2020-08-20最高法明确以一年期贷款市场报价利率（LPR）的4倍为标准确定民间借贷利率的司法保护上线。15.4%这个数字突然进入了大家的视野，当然还有APR和IRR。到底是哪个口径的15.4%，引起了圈内人的激烈讨论。今天我们不聊到底哪个口径是监管的意中人，我们先把APR和IRR这两个口径的计算逻辑和区别讲清楚，便于大家可以自行预测后续的发展。1IRR计算IRR：内部收益率（Internal Rate of Return）就是资金流入现值总额与资金流出现值总额相等、净现值等于零时的折现率。关键是要考虑现金流与净现值的折现。考虑现金流可以理解为期初我借出了一笔款，分12期，此时期初资金是流出的，但随着时间的推移，每个月我都有本金和利息的回款，这个时候每个月我们都有资金的流入。资金回流的节奏会影响我手上可用资金池的大小，如果我资金充裕，可以进行另外一项投资。因为有通货膨胀，所以今年1W大洋可购买的实物，5年后可能只能买到其中的一部分。也就意味着我们借出去的款，最后回收之后需要折算到放款时的现值，才能知道我们到底有没有跑赢通货膨胀？或者说快了多少？这就是净现值的折现。接下来我们看看怎么计算IRR，其实Excel中有现成的函数可以使用。我们假设一笔12W的借款，分12期，以等额本息的方式进行还款，以IRR=15.4%来计算：Step1:计算月度费率IRR（年化）=15.4%IRR（月）=15.4%/12=1.283%Step2:计算月度还款计划因为需要计算现金流，所以我们需要计算出每月的还款金额。这里推荐大家两个计算等额本息还款计划的Excel内置函数：关注“金科应用研院”，回复“ZH”领取风控资料合集PPMT（月利率，期数，总期限，贷款本金）：计算月还款本金IPMT（月利率，期数，总期限，-贷款本金）：计算月还款利息然后我们再计算 月还款额=月还款本金+月还款利息，结果如下：Step3:计算IRR这里直接使用Excel的内置函数IRR（）就可以了，结果如下：IRR年化=（现金流范围）*12这里要注意以下几点：IRR（）函数要把期数从0-12对应的现金流单元格全部计算进来IRR年化/12 就得到IRR月度费率如果已有了月度还款额就可以直接反推IRR（年化）我们同步也计算了下此时APR的年化，相比IRR年化要小了很多，可见两种口径差异还是很大的。如果IRR（年化）=15.4%，那么APR（年化）=8.534%2APR计算APR：年度利率（Annual Percentage Rate）可以的直观的理解为，我借了一笔款，最终我能收到多少的利息，用这个利息除以我的借款本金就得到了APR的利率。这个口径的优势是便于理解，计算方式简单粗暴，能让客户很快的了解到他最终需要支付多少利息。接下来我们看看怎么计算APR。我们同样假设一笔12W的借款，分12期，以APR=15.4%来计算：Step1:计算月度费率APR（年化）=15.4%APR（月）=15.4%/12=1.283%Step2:计算月度还款计划月还款本金=贷款本金/12月还款利息=贷款本金* APR（月）月还款额=月还款本金+月还款利息，结果如下：Step3:计算APRAPR（年化）=合计总利息/贷款本金APR（月）= APR（年化）/12同时我们也计算下此时的IRR，结果如下：其实APR的计算不需要计算月还款额，我们这里计算是想让大家更直观的对比APR和IRR的差异。计算后发现，如果APR（年化）=15.4%，那么IRR（年化）=27.299%。不管最终是哪种口径的费率，我个人都希望监管机构能尽快梳理各层级机构的利率梯度。并明确此次调整的方向，引导市场有序的朝健康的方向发展；同时各机构也要做好针对严格口径的应对方案，凛冬将至！关注“金科应用研院”，回复“ZH”领取风控资料合集发布于 2020-09-09 14:45互联网金融大数据​赞同 26​​6 条评论​分享​喜欢​收藏​申请转载​文章被以下专栏收录来FAL学风险控制风控干货知

APR中文(简体)翻译：剑桥词典

APR中文(简体)翻译：剑桥词典

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APR 在英语-中文（简体）词典中的翻译

APRnoun [ S ] uk

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/ˌeɪ.piˈɑːr/ us

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/ˌeɪ.piˈɑːr/

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abbreviation for Annual Percentage Rate: the rate at which someone who borrows money is charged, calculated over a period of twelve months

年率，年利率（Annual Percentage Rate的缩写）

The interest rate on my credit card is currently 25.5 percent APR.

目前我的信用卡贷款年利率是25.5%。

(APR在剑桥英语-中文（简体）词典的翻译 © Cambridge University Press)

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APR的翻译

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年率，年利率（Annual Percentage Rate的縮寫）…

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西班牙语

forma abreviada de “Annual Percentage Rate”:, TAE, abril…

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forma abreviada de “Annual Percentage Rate”:, Taxa Anual Efectiva Global, TAEG…

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in Ukrainian

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nisan…

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avril…

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apr., april…

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Apr…

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kwiec. (= = kwiecień), kwiec.…

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april…

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April…

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approximate

approximately

approximation

appurtenance

APR

après-ski

apricot

April

April fool

APR更多的中文(简体)翻译

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Apr., at April

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“每日一词”

veggie burger

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/ˈvedʒ.i ˌbɜː.ɡər/

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/ˈvedʒ.i ˌbɝː.ɡɚ/

a type of food similar to a hamburger but made without meat, by pressing together small pieces of vegetables, seeds, etc. into a flat, round shape

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APR计算器 - 计算年度百分比率

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APR计算器 - 计算年度百分比率

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  APR计算器计算年度百分比率（APR） APR计算器

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年利率: %

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Embed APR计算器 Widget APR计算器 APR计算器用于计算年度百分比率（APR）。 APR定义年度百分比率（APR）描述了一年的利率，而不仅仅是月度利率，适用于贷款，抵押贷款，汽车贷款，信用卡等。考虑到所有额外费用，APR是等价利率收取一定的贷款金额。它是贷款金额，利率，总额外费用和条款的函数。如果给定贷款没有增加成本，则APR将等于利率。 Reference this content, page, or tool as: "APR计算器" at https://miniwebtool.com/zh-cn/apr-calculator/ from miniwebtool, https://miniwebtool.com/ 其他相关工具: APY计算器  利息率计算工具:

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年度利率_百度百科

_百度百科 网页新闻贴吧知道网盘图片视频地图文库资讯采购百科百度首页登录注册进入词条全站搜索帮助首页秒懂百科特色百科知识专题加入百科百科团队权威合作下载百科APP个人中心收藏查看我的收藏0有用+10年度利率播报讨论上传视频利息计算年利率名词年度利率，简称APR，英文为Annual Percentage Rate，是利息计算年利率名词。简单的说，利息年利率就是APR。中文名年度利率外文名Annual Percentage Rate简    称APR释    义利息计算年利率名词分类1. 信用卡年度利率信用卡年度利率中牵扯到几个不同的APR概念：多个年度利率、惩罚性的年度利率、新客户的年度利率、延迟实施的年度利率、固定与变动的年度利率，下面依次阐述：2. 多个年度利率多个年度利率多个年度利率多个年度利率：一张信用卡可能有多个APR。一个APR用来购买，另一个用来提取垫款，另外一个用来转移收支。提取垫款和转移收支的APR通常比购买的APR要高。例如购买的是14%，垫款的是18%，转移收支是19%。3. 惩罚性的年度利率惩罚性的年度利率(A penalty APR)：如果你过期付款，年度利率会升高。例如你的信用卡条款里面会这样写，"如果你在半年之内延迟付款两次，收到的时间比预定的日期晚了10天以上，你将被通知使用惩罚性的年度利率。"4. 新客户的年度利率新客户的年度利率(An introductory APR)：当新客户的优惠年度利率到期后，将会有一个不同的年度利率。5. 延迟实施的年度利率延迟实施的年度利率(A delayed APR)：未来将使用一个不同的年度利率 。例如一个信用卡可能做广告，宣称在3月以前免交利息。 那么就看看3月以后是什么利息。6. 固定与变动的年度利率固定与变动的年度利率(Fixed vs. variable APR)：有些信用卡是固定的利率，年度利率 (APR) 不变或者很少变化。然而即使固定的利率，时间长久也是会变的。不过信用卡公司在增加固定的利率以前必须要通知客户。新手上路成长任务编辑入门编辑规则本人编辑我有疑问内容质疑在线客服官方贴吧意见反馈投诉建议举报不良信息未通过词条申诉投诉侵权信息封禁查询与解封©2024 Baidu 使用百度前必读 | 百科协议 | 隐私政策 | 百度百科合作平台 | 京ICP证030173号 京公网安备110000020000

Annual Percentage Rate (APR): What It Means and How It Works

Annual Percentage Rate (APR): What It Means and How It Works

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Table of Contents

Annual Percentage Rate (APR)

How APR Works

Types of APRs

APR vs. APY

APR vs. Nominal vs. Daily Rate

Disadvantages of APR

Frequently Asked Questions

The Bottom Line

Personal Finance

Banking

Annual Percentage Rate (APR): What It Means and How It Works

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Updated February 26, 2024

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What Is Annual Percentage Rate (APR)?

Annual percentage rate (APR) refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment. This includes any fees or additional costs associated with the transaction but does not take compounding into account. The APR provides consumers with a bottom-line number they can compare among lenders, credit cards, or investment products.

Spanish Translation of Annual Percentage Rate (APR)

Key Takeaways

An annual percentage rate (APR) is the yearly rate charged for a loan or earned by an investment and includes interest and fees.Financial institutions must disclose a financial instrument’s APR before any agreement is signed.The APR provides a consistent basis for presenting annual interest rate information in order to protect consumers from misleading advertising.An APR may not reflect the actual cost of borrowing because lenders have a fair amount of leeway in calculating it, excluding certain fees.APR shouldn't be confused with APY (annual percentage yield), a calculation that takes the compounding of interest into account.

How the Annual Percentage Rate (APR) Works

An annual percentage rate is expressed as an interest rate. It calculates what percentage of the principal you’ll pay each year by taking things such as monthly payments and fees into account. APR is also the annual rate of interest paid on investments without accounting for the compounding of interest within that year.

The Truth in Lending Act (TILA) of 1968 mandates that lenders disclose the APR they charge to borrowers. Credit card companies are allowed to advertise interest rates on a monthly basis, but they must clearly report the APR to customers before they sign an agreement.

Credit card companies can increase your interest rate for new purchases, but not existing balances if they provide you with 45 days' notice first.

How Is APR Calculated?

APR is calculated by multiplying the periodic interest rate by the number of periods in a year in which it was applied. It does not indicate how many times the rate is actually applied to the balance.

APR

=

(

(

Fees

+

Interest

Principal

n

)

×

365

)

×

100

where:

Interest

=

Total interest paid over life of the loan

Principal

=

Loan amount

n

=

Number of days in loan term

\begin{aligned} &\text{APR} = \left ( \left ( \frac{ \frac{ \text{Fees} + \text{Interest} }{ \text {Principal} } }{ n } \right ) \times 365 \right ) \times 100 \\ &\textbf{where:} \\ &\text{Interest} = \text{Total interest paid over life of the loan} \\ &\text{Principal} = \text{Loan amount} \\ &n = \text{Number of days in loan term} \\ \end{aligned}

​APR=((nPrincipalFees+Interest​​)×365)×100where:Interest=Total interest paid over life of the loanPrincipal=Loan amountn=Number of days in loan term​

Types of APRs

Credit card APRs vary based on the type of charge. The credit card issuer may charge one APR for purchases, another for cash advances, and yet another for balance transfers from another card. Issuers also charge high-rate penalty APRs to customers for late payments or violating other terms of the cardholder agreement. There’s also the introductory APR—a low or 0% rate—with which many credit card companies try to entice new customers to sign up for a card.

Bank loans generally come with either fixed or variable APRs. A fixed APR loan has an interest rate that is guaranteed not to change during the life of the loan or credit facility. A variable APR loan has an interest rate that may change at any time.

The APR borrowers are charged also depends on their credit. The rates offered to those with excellent credit are significantly lower than those offered to those with bad credit.

Compound Interest or Simple Interest?

APR does not take into account the compounding of interest within a specific year: It is based only on simple interest.

APR vs. Annual Percentage Yield (APY)

Though an APR only accounts for simple interest, the annual percentage yield (APY) takes compound interest into account. As a result, a loan’s APY is higher than its APR. The higher the interest rate—and to a lesser extent, the smaller the compounding periods—the greater the difference between the APR and APY.

Imagine that a loan’s APR is 12%, and the loan compounds once a month. If an individual borrows $10,000, their interest for one month is 1% of the balance, or $100. That effectively increases the balance to $10,100. The following month, 1% interest is assessed on this amount, and the interest payment is $101, slightly higher than it was the previous month. If you carry that balance for the year, your effective interest rate becomes 12.68%. APY includes these small shifts in interest expenses due to compounding, while APR does not.

Here's another way to look at it. Say you compare an investment that pays 5% per year with one that pays 5% monthly. For the first month, the APY equals 5%, the same as the APR. But for the second, the APY is 5.12%, reflecting the monthly compounding.

Given that an APR and a different APY can represent the same interest rate on a loan or financial product, lenders often emphasize the more flattering number, which is why the Truth in Savings Act of 1991 mandated both APR and APY disclosure in ads, contracts, and agreements. A bank will advertise a savings account’s APY in a large font and its corresponding APR in a smaller one, given that the former features a superficially larger number. The opposite happens when the bank acts as the lender and tries to convince its borrowers that it’s charging a low rate. A great resource for comparing both APR and APY rates on a mortgage is a mortgage calculator.

APR vs. APY Example

Let's say that XYZ Corp. offers a credit card that levies interest of 0.06273% daily. Multiply that by 365, and that’s 22.9% per year, which is the advertised APR. Now, if you were to charge a different $1,000 item to your card every day and waited until the day after the due date (when the issuer started levying interest) to start making payments, you’d owe $1,000.6273 for each thing you bought.

To calculate the APY or effective annual interest rate—the more typical term for credit cards—add one (that represents the principal) and take that number to the power of the number of compounding periods in a year; subtract one from the result to get the percentage:

APY

=

(

1

+

Periodic Rate

)

n

−

1

where:

n

=

Number of compounding periods per year

\begin{aligned} &\text{APY} = (1 + \text{Periodic Rate} ) ^ n - 1 \\ &\textbf{where:} \\ &n = \text{Number of compounding periods per year} \\ \end{aligned}

​APY=(1+Periodic Rate)n−1where:n=Number of compounding periods per year​

In this case your APY or EAR would be 25.7%:

(

(

1

+

.

0006273

)

365

)

−

1

=

.

257

\begin{aligned} &( ( 1 + .0006273 ) ^ {365} ) - 1 = .257 \\ \end{aligned}

​((1+.0006273)365)−1=.257​

If you only carry a balance on your credit card for one month’s period, you will be charged the equivalent yearly rate of 22.9%. However, if you carry that balance for the year, your effective interest rate becomes 25.7% as a result of compounding each day.

APR vs. Nominal Interest Rate vs. Daily Periodic Rate

An APR tends to be higher than a loan’s nominal interest rate. That’s because the nominal interest rate doesn’t account for any other expense accrued by the borrower. The nominal rate may be lower on your mortgage if you don’t account for closing costs, insurance, and origination fees. If you end up rolling these into your mortgage, your mortgage balance increases, as does your APR.

The daily periodic rate, on the other hand, is the interest charged on a loan’s balance on a daily basis—the APR divided by 365. Lenders and credit card providers are allowed to represent APR on a monthly basis, though, as long as the full 12-month APR is listed somewhere before the agreement is signed.

Disadvantages of Annual Percentage Rate (APR)

The APR isn’t always an accurate reflection of the total cost of borrowing. In fact, it may understate the actual cost of a loan. That’s because the calculations assume long-term repayment schedules. The costs and fees are spread too thin with APR calculations for loans that are repaid faster or have shorter repayment periods. For instance, the average annual impact of mortgage closing costs is much smaller when those costs are assumed to have been spread over 30 years instead of seven to 10 years.

Who Calculates APR?

Lenders have a fair amount of authority to determine how to calculate the APR, including or excluding different fees and charges.

APR also runs into some trouble with adjustable-rate mortgages (ARMs). Estimates always assume a constant rate of interest, and even though APR takes rate caps into consideration, the final number is still based on fixed rates. Because the interest rate on an ARM will change when the fixed-rate period is over, APR estimates can severely understate the actual borrowing costs if mortgage rates rise in the future.

Mortgage APRs may or may not include other charges, such as appraisals, titles, credit reports, applications, life insurance, attorneys and notaries, and document preparation. There are other fees that are deliberately excluded, including late fees and other one-time fees.

All this may make it difficult to compare similar products because the fees included or excluded differ from institution to institution. In order to accurately compare multiple offers, a potential borrower must determine which of these fees are included and, to be thorough, calculate APR using the nominal interest rate and other cost information.

Why Is the Annual Percentage Rate (APR) Disclosed?

Consumer protection laws require companies to disclose the APRs associated with their product offerings in order to prevent companies from misleading customers. For instance, if they were not required to disclose the APR, a company might advertise a low monthly interest rate while implying to customers that it was an annual rate. This could mislead a customer into comparing a seemingly low monthly rate against a seemingly high annual one. By requiring all companies to disclose their APRs, customers are presented with an “apples to apples” comparison.

What Is a Good APR?

What counts as a “good” APR will depend on factors such as the competing rates offered in the market, the prime interest rate set by the central bank, and the borrower’s own credit score. When prime rates are low, companies in competitive industries will sometimes offer very low APRs on their credit products, such as the 0% on car loans or lease options. Although these low rates might seem attractive, customers should verify whether these rates last for the full length of the product’s term, or whether they are simply introductory rates that will revert to a higher APR after a certain period has passed. Moreover, low APRs may only be available to customers with especially high credit scores.

How Do You Calculate APR?

The formula for calculating APR is straightforward. It consists of multiplying the periodic interest rate by the number of periods in a year in which the rate is applied. The exact formula is as follows:APR=((Fees+InterestPrincipaln)×365)×100where:Interest=Total interest paid over life of the loanPrincipal=Loan amountn=Number of days in loan term\begin{aligned} &\text{APR} = \left ( \left ( \frac{ \frac{ \text{Fees} + \text{Interest} }{ \text {Principal} } }{ n } \right ) \times 365 \right ) \times 100 \\ &\textbf{where:} \\ &\text{Interest} = \text{Total interest paid over life of the loan} \\ &\text{Principal} = \text{Loan amount} \\ &n = \text{Number of days in loan term} \\ \end{aligned}​APR=((nPrincipalFees+Interest​​)×365)×100where:Interest=Total interest paid over life of the loanPrincipal=Loan amountn=Number of days in loan term​

The Bottom Line

The APR is the basic theoretical cost or benefit of money loaned or borrowed. By calculating only the simple interest without periodic compounding, the APR gives borrowers and lenders a snapshot of how much interest they are earning or paying within a certain period of time. If someone is borrowing money, such as by using a credit card or applying for a mortgage, the APR can be misleading because it only presents the base number of what they are paying without taking time into the equation. Conversely, if someone is looking at the APR on a savings account, it doesn't illustrate the full impact of interest earned over time.

APRs are often a selling point for different financial instruments, such as mortgages or credit cards. When choosing a tool with an APR, be careful to also take into account the APY because it will prove a more accurate number for what you will pay or earn over time. Though the formula for your APR may stay the same, different financial institutions will include different fees in the principal balance. Be aware of what is included in your APR when signing any agreement.

Article Sources

Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our

editorial policy.

Federal Register. "Truth in Lending (Regulation Z)."

Federal Trade Commission. "Truth in Lending Act."

Consumer Financial Protection Bureau. "When Can my Credit Card Company Increase my Interest Rate?"

Consumer Financial Protection Bureau. "Part 1030—Truth in Savings (Regulation DD)."

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Annual Equivalent Rate (AER): Definition, Formula, Examples

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