[{"data":1,"prerenderedAt":517},["ShallowReactive",2],{"calc-page":3,"SmbK7mgVbm":272,"related-calculators":463},{"id":4,"title":5,"body":6,"description":15,"extension":266,"meta":267,"navigation":268,"path":269,"seo":270,"stem":271},"zh_categories/zh/categories/finance/simple-vs-compound-interest-calculator.md","单利与复利计算器",{"type":7,"value":8,"toc":247},"minimal",[9,12,16,19,24,31,37,52,63,68,74,77,117,120,125,128,132,135,139,142,146,149,153,156,160,167,173,176,179,182,212,215,241,244],[10,11,5],"h1",{"id":5},[13,14,15],"p",{},"两笔贷款或储蓄账户可能标示着完全相同的利率,最终结果却大相径庭——这取决于计息方式是单利还是复利。用下方计算器看看你的钱会如何随时间复利增长,再结合下面的手工对比,准确了解单利情形下你会多拿到(或少拿到)多少钱。",[17,18],"calculator-compoundinterest",{},[20,21,23],"h2",{"id":22},"单利与复利真正的区别是什么","单利与复利:真正的区别是什么?",[13,25,26,30],{},[27,28,29],"strong",{},"单利","在整个期限内始终只按最初的本金计算,不论资金存放多久、已经产生过多少次利息,计息基数都不会改变。计算公式为:",[13,32,33],{},[34,35,36],"code",{},"A = P × (1 + r × t)",[13,38,39,40,43,44,47,48,51],{},"其中",[34,41,42],{},"P","是本金,",[34,45,46],{},"r","是年利率(以小数表示),",[34,49,50],{},"t","是年数。",[13,53,54,57,58,62],{},[27,55,56],{},"复利","——上面的计算器模拟的正是这种方式——是在本金",[59,60,61],"em",{},"加上","每个计息周期已经产生的利息基础上计算的。每次利息被计入余额后,下一期的利息就会在这个更大的金额上计算——所以计息时间越长,余额增长得越快,单利与复利结果之间的差距也会逐年扩大。计算公式为:",[13,64,65],{},[34,66,67],{},"A = P × (1 + r/n)^(n×t)",[13,69,39,70,73],{},[34,71,72],{},"n","是每年的计息周期数。",[20,75,76],{"id":76},"单利与复利的主要区别",[78,79,80,87,93,99,105,111],"ul",{},[81,82,83,86],"li",{},[27,84,85],{},"增长曲线",":单利呈直线增长;复利呈随时间逐渐变陡的曲线增长。",[81,88,89,92],{},[27,90,91],{},"计息基数",":单利始终只按最初的本金计算;复利按本金加上此前所有已计入的利息计算。",[81,94,95,98],{},[27,96,97],{},"时间的影响",":时间跨度越长,两者的差距越大——短期内差异很小,但几十年后差距会变得极其巨大。",[81,100,101,104],{},[27,102,103],{},"计息频率的影响",":对复利而言,计息越频繁(按日、按月还是按年),在相同名义年利率下实际收益会略高一些。",[81,106,107,110],{},[27,108,109],{},"各自常见的应用场景",":复利是储蓄账户、信用卡和大多数投资账户的标准计息方式;单利常见于部分汽车贷款、短期个人贷款以及某些债券。",[81,112,113,116],{},[27,114,115],{},"谁更受益",":单利对借款人更有利(你只对最初借出的金额支付利息);复利对储户和投资者更有利(你的收益本身也会产生收益)。",[20,118,119],{"id":119},"如何用这个计算器比较两者",[121,122,124],"h3",{"id":123},"_1-输入本金利率和时间跨度","1. 输入本金、利率和时间跨度",[13,126,127],{},"输入起始本金、年利率和年数,并选择一个计息频率(例如按月或按年)。若想做纯粹的一次性本金对比,把每月供款设为0。",[121,129,131],{"id":130},"_2-查看复利结果","2. 查看复利结果",[13,133,134],{},"计算器最终显示的余额和年度图表,展示了本金在你所选计息频率下按复利增长的过程。",[121,136,138],{"id":137},"_3-手动计算单利结果","3. 手动计算单利结果",[13,140,141],{},"用同样的本金、利率和年数,套用上面的单利公式:本金乘以(1加上利率乘以年数)。这就是同一笔钱在完全不计复利的情况下,按单利会增长到的金额。",[121,143,145],{"id":144},"_4-比较差距","4. 比较差距",[13,147,148],{},"用复利结果减去单利结果。这个差值就是复利在同一时间段内多产生的收益——你会发现,时间跨度越长或利率越高,这个差距就越大。",[121,150,152],{"id":151},"_5-尝试不同的计息频率","5. 尝试不同的计息频率",[13,154,155],{},"在本金、利率和年数不变的情况下,把计息频率在按年、按月、按日之间切换。你会看到,即便标示的年利率没有变化,计息越频繁,复利结果就会略高一些——这就是名义利率与实际年化收益率之间的差别。",[20,157,159],{"id":158},"对你来说哪个更重要","对你来说哪个更重要?",[13,161,162,163,166],{},"如果你在",[27,164,165],{},"借钱",",单利总体上对你更有利,因为你只需为最初借出的本金支付利息,而不是为已经产生的利息再付利息。比较贷款方案时,一定要确认利息是单利还是复利(如果是复利,计息频率是多少)——一笔标称单利利率略高的贷款,总成本可能反而低于计息频繁的较低复利贷款。",[13,168,162,169,172],{},[27,170,171],{},"储蓄或投资",",复利对你有利,而且计息越频繁越好。尽早开始在这里格外重要:同样的钱,能复利增长的年数越多,增长幅度就越不成比例地超过晚些时候才投入的同等金额,即便利率相同。",[20,174,175],{"id":175},"目标关键词",[13,177,178],{},"单利vs复利计算器,单利计算器,复利计算器,利息对比计算器,单利与复利的区别",[20,180,181],{"id":181},"处理利息计算的建议",[183,184,185,191,197,206],"ol",{},[81,186,187,190],{},[27,188,189],{},"一定要确认计息方式",":贷款或账户标示的年利率并不能说明全部情况——一定要问清是单利还是复利,如果是复利,计息频率是多少。",[81,192,193,196],{},[27,194,195],{},"尽早开始复利",":由于复利增长会随时间加速,长期储蓄最大的杠杆通常是时间,而不是稍高一点的利率。",[81,198,199,202,205],{},[27,200,201],{},"关注实际年化收益率(APY)而非名义利率",[203,204],"apy",{},"已经把计息频率计算在内,是比较储蓄产品更准确的指标;年利率(APR)则没有。",[81,207,208,211],{},[27,209,210],{},"让利息留存再投资,而非提取",":复利增长只有在已赚取的利息留在账户内时才能持续——一有利息就提取,实际上会把复利账户变成单利账户。",[20,213,214],{"id":214},"常见误区",[78,216,217,223,229,235],{},[81,218,219,222],{},[27,220,221],{},"默认所有利息都是复利",":一些短期贷款确实使用单利计息——如果按复利来估算,会高估你实际要偿还的金额。",[81,224,225,228],{},[27,226,227],{},"只比较利率而不比较计息频率",":按日计息的5%利率,实际收益会高于按年计息的5%利率。",[81,230,231,234],{},[27,232,233],{},"低估长期时间跨度的影响",":由于复利增长是指数级的,20到30年后的效果远比基于几年经验的直觉判断要大得多。",[81,236,237,240],{},[27,238,239],{},"忽视侵蚀复利的费用",":账户费用或较高的费用率会降低实际增长率,并可能显著削弱长期复利收益。",[20,242,243],{"id":243},"结语",[13,245,246],{},"完全相同的利率、本金和时间跨度,在单利和复利下可能产生天差地别的结果——唯一的区别在于利息是否会产生利息。用上面的计算器查看你的复利增长情况,再用同样的数字手工套用单利公式,让这个差距的大小来指引你判断,哪种贷款或储蓄产品真正对你更有利。",{"title":248,"searchDepth":249,"depth":249,"links":250},"",2,[251,252,253,261,262,263,264,265],{"id":22,"depth":249,"text":23},{"id":76,"depth":249,"text":76},{"id":119,"depth":249,"text":119,"children":254},[255,257,258,259,260],{"id":123,"depth":256,"text":124},3,{"id":130,"depth":256,"text":131},{"id":137,"depth":256,"text":138},{"id":144,"depth":256,"text":145},{"id":151,"depth":256,"text":152},{"id":158,"depth":249,"text":159},{"id":175,"depth":249,"text":175},{"id":181,"depth":249,"text":181},{"id":214,"depth":249,"text":214},{"id":243,"depth":249,"text":243},"md",{},true,"/zh/categories/finance/simple-vs-compound-interest-calculator",{"title":5,"description":15},"zh/categories/finance/simple-vs-compound-interest-calculator",{"Automotive":273,"Conversions":282,"Cooking":295,"Finance":308,"Fitness":419,"Health":432,"Math":441,"Time":454},[274,278],{"title":275,"path":276,"stem":277},"燃油成本计算器","/zh/categories/automotive/fuel-cost-calculator","zh/categories/automotive/fuel-cost-calculator",{"title":279,"path":280,"stem":281},"轮胎尺寸计算器","/zh/categories/automotive/tire-size-calculator","zh/categories/automotive/tire-size-calculator",[283,287,291],{"title":284,"path":285,"stem":286},"货币汇率转换计算器","/zh/categories/conversions/currency-conversion-calculator","zh/categories/conversions/currency-conversion-calculator",{"title":288,"path":289,"stem":290},"单位换算计算器","/zh/categories/conversions/unit-conversion-calculator","zh/categories/conversions/unit-conversion-calculator",{"title":292,"path":293,"stem":294},"重量换算计算器","/zh/categories/conversions/weight-conversion-calculator","zh/categories/conversions/weight-conversion-calculator",[296,300,304],{"title":297,"path":298,"stem":299},"空气炸锅换算计算器","/zh/categories/cooking/air-fryer-conversion-calculator","zh/categories/cooking/air-fryer-conversion-calculator",{"title":301,"path":302,"stem":303},"厨房计量单位换算计算器","/zh/categories/cooking/kitchen-measurement-converter-calculator","zh/categories/cooking/kitchen-measurement-converter-calculator",{"title":305,"path":306,"stem":307},"食谱换算计算器","/zh/categories/cooking/recipe-scaler-calculator","zh/categories/cooking/recipe-scaler-calculator",[309,314,318,322,327,331,336,341,345,349,353,357,361,366,370,374,378,382,386,390,394,398,402,406,410,414,415],{"title":310,"path":311,"stem":312,"subcategory":313},"15年期与30年期房贷计算器","/zh/categories/finance/15-year-vs-30-year-mortgage-calculator","zh/categories/finance/15-year-vs-30-year-mortgage-calculator","loans",{"title":315,"path":316,"stem":317,"subcategory":313},"飞机贷款计算器","/zh/categories/finance/aircraft-loan-calculator","zh/categories/finance/aircraft-loan-calculator",{"title":319,"path":320,"stem":321,"subcategory":313},"汽车贷款计算器","/zh/categories/finance/auto-loan-calculator","zh/categories/finance/auto-loan-calculator",{"title":323,"path":324,"stem":325,"subcategory":326},"比特币挖矿收益计算器","/zh/categories/finance/bitcoin-mining-calculator","zh/categories/finance/bitcoin-mining-calculator","businessDeals",{"title":328,"path":329,"stem":330,"subcategory":313},"现金再融资与HELOC计算器","/zh/categories/finance/cash-out-refinance-vs-heloc-calculator","zh/categories/finance/cash-out-refinance-vs-heloc-calculator",{"title":332,"path":333,"stem":334,"subcategory":335},"复利计算器","/zh/categories/finance/compound-interest-calculator","zh/categories/finance/compound-interest-calculator","investingRetirement",{"title":337,"path":338,"stem":339,"subcategory":340},"电费计算器","/zh/categories/finance/electricity-calculator","zh/categories/finance/electricity-calculator","incomeUtilities",{"title":342,"path":343,"stem":344,"subcategory":313},"农用设备与拖拉机贷款计算器","/zh/categories/finance/equipment-tractor-loan-calculator","zh/categories/finance/equipment-tractor-loan-calculator",{"title":346,"path":347,"stem":348,"subcategory":313},"电动汽车（EV）贷款计算器","/zh/categories/finance/ev-loan-calculator","zh/categories/finance/ev-loan-calculator",{"title":350,"path":351,"stem":352,"subcategory":335},"金融计算器（货币时间价值）","/zh/categories/finance/financial-calculator","zh/categories/finance/financial-calculator",{"title":354,"path":355,"stem":356,"subcategory":313},"固定利率与浮动利率房贷计算器","/zh/categories/finance/fixed-vs-adjustable-rate-mortgage-calculator","zh/categories/finance/fixed-vs-adjustable-rate-mortgage-calculator",{"title":358,"path":359,"stem":360,"subcategory":340},"计算器","/zh/categories/finance/handheld-calculator","zh/categories/finance/handheld-calculator",{"title":362,"path":363,"stem":364,"subcategory":365},"伊斯兰金融（穆拉巴哈）计算器","/zh/categories/finance/islamic-finance-calculator","zh/categories/finance/islamic-finance-calculator","islamicFinance",{"title":367,"path":368,"stem":369,"subcategory":313},"租赁月供计算器","/zh/categories/finance/lease-payment-calculator","zh/categories/finance/lease-payment-calculator",{"title":371,"path":372,"stem":373,"subcategory":313},"租车与买车计算器","/zh/categories/finance/lease-vs-buy-car-calculator","zh/categories/finance/lease-vs-buy-car-calculator",{"title":375,"path":376,"stem":377,"subcategory":326},"利曼公式计算器","/zh/categories/finance/lehman-calculator","zh/categories/finance/lehman-calculator",{"title":379,"path":380,"stem":381,"subcategory":313},"贷款计算器","/zh/categories/finance/loan-calculator","zh/categories/finance/loan-calculator",{"title":383,"path":384,"stem":385,"subcategory":313},"按揭计算器","/zh/categories/finance/mortgage-calculator","zh/categories/finance/mortgage-calculator",{"title":387,"path":388,"stem":389,"subcategory":313},"摩托车贷款计算器","/zh/categories/finance/motorcycle-loan-calculator","zh/categories/finance/motorcycle-loan-calculator",{"title":391,"path":392,"stem":393,"subcategory":313},"个人贷款与信用卡计算器","/zh/categories/finance/personal-loan-vs-credit-card-calculator","zh/categories/finance/personal-loan-vs-credit-card-calculator",{"title":395,"path":396,"stem":397,"subcategory":313},"房地产投资融资计算器","/zh/categories/finance/real-estate-financing-calculator","zh/categories/finance/real-estate-financing-calculator",{"title":399,"path":400,"stem":401,"subcategory":335},"Roth IRA 转换计算器","/zh/categories/finance/roth-ira-conversion-calculator","zh/categories/finance/roth-ira-conversion-calculator",{"title":403,"path":404,"stem":405,"subcategory":335},"罗斯与传统个人退休账户(IRA)计算器","/zh/categories/finance/roth-vs-traditional-ira-calculator","zh/categories/finance/roth-vs-traditional-ira-calculator",{"title":407,"path":408,"stem":409,"subcategory":313},"房车与露营拖车贷款计算器","/zh/categories/finance/rv-camper-loan-calculator","zh/categories/finance/rv-camper-loan-calculator",{"title":411,"path":412,"stem":413,"subcategory":340},"薪资计算器","/zh/categories/finance/salary-calculator","zh/categories/finance/salary-calculator",{"title":5,"path":269,"stem":271,"subcategory":335},{"title":416,"path":417,"stem":418,"subcategory":313},"卡车贷款计算器","/zh/categories/finance/truck-loan-calculator","zh/categories/finance/truck-loan-calculator",[420,424,428],{"title":421,"path":422,"stem":423},"消耗卡路里计算器","/zh/categories/fitness/calories-burned-calculator","zh/categories/fitness/calories-burned-calculator",{"title":425,"path":426,"stem":427},"单次最大重量(1RM)计算器","/zh/categories/fitness/one-rep-max-calculator","zh/categories/fitness/one-rep-max-calculator",{"title":429,"path":430,"stem":431},"目标心率计算器","/zh/categories/fitness/target-heart-rate-calculator","zh/categories/fitness/target-heart-rate-calculator",[433,437],{"title":434,"path":435,"stem":436},"BMI 计算器","/zh/categories/health/bmi-calculator","zh/categories/health/bmi-calculator",{"title":438,"path":439,"stem":440},"每日卡路里计算器","/zh/categories/health/calorie-calculator","zh/categories/health/calorie-calculator",[442,446,450],{"title":443,"path":444,"stem":445},"圆周长计算器","/zh/categories/math/circumference-calculator","zh/categories/math/circumference-calculator",{"title":447,"path":448,"stem":449},"勾股定理计算器","/zh/categories/math/pythagorean-calculator","zh/categories/math/pythagorean-calculator",{"title":451,"path":452,"stem":453},"美国退伍军人事务部（VA）伤残等级综合计算器","/zh/categories/math/va-disability-calculator","zh/categories/math/va-disability-calculator",[455,459],{"title":456,"path":457,"stem":458},"工作日计算器","/zh/categories/time/business-days-calculator","zh/categories/time/business-days-calculator",{"title":460,"path":461,"stem":462},"日期间隔计算器","/zh/categories/time/date-duration-calculator","zh/categories/time/date-duration-calculator",{"Automotive":464,"Conversions":467,"Cooking":471,"Finance":475,"Fitness":503,"Health":507,"Math":510,"Time":514},[465,466],{"title":275,"path":276,"stem":277},{"title":279,"path":280,"stem":281},[468,469,470],{"title":284,"path":285,"stem":286},{"title":288,"path":289,"stem":290},{"title":292,"path":293,"stem":294},[472,473,474],{"title":297,"path":298,"stem":299},{"title":301,"path":302,"stem":303},{"title":305,"path":306,"stem":307},[476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502],{"title":310,"path":311,"stem":312,"subcategory":313},{"title":315,"path":316,"stem":317,"subcategory":313},{"title":319,"path":320,"stem":321,"subcategory":313},{"title":323,"path":324,"stem":325,"subcategory":326},{"title":328,"path":329,"stem":330,"subcategory":313},{"title":332,"path":333,"stem":334,"subcategory":335},{"title":337,"path":338,"stem":339,"subcategory":340},{"title":342,"path":343,"stem":344,"subcategory":313},{"title":346,"path":347,"stem":348,"subcategory":313},{"title":350,"path":351,"stem":352,"subcategory":335},{"title":354,"path":355,"stem":356,"subcategory":313},{"title":358,"path":359,"stem":360,"subcategory":340},{"title":362,"path":363,"stem":364,"subcategory":365},{"title":367,"path":368,"stem":369,"subcategory":313},{"title":371,"path":372,"stem":373,"subcategory":313},{"title":375,"path":376,"stem":377,"subcategory":326},{"title":379,"path":380,"stem":381,"subcategory":313},{"title":383,"path":384,"stem":385,"subcategory":313},{"title":387,"path":388,"stem":389,"subcategory":313},{"title":391,"path":392,"stem":393,"subcategory":313},{"title":395,"path":396,"stem":397,"subcategory":313},{"title":399,"path":400,"stem":401,"subcategory":335},{"title":403,"path":404,"stem":405,"subcategory":335},{"title":407,"path":408,"stem":409,"subcategory":313},{"title":411,"path":412,"stem":413,"subcategory":340},{"title":5,"path":269,"stem":271,"subcategory":335},{"title":416,"path":417,"stem":418,"subcategory":313},[504,505,506],{"title":421,"path":422,"stem":423},{"title":425,"path":426,"stem":427},{"title":429,"path":430,"stem":431},[508,509],{"title":434,"path":435,"stem":436},{"title":438,"path":439,"stem":440},[511,512,513],{"title":443,"path":444,"stem":445},{"title":447,"path":448,"stem":449},{"title":451,"path":452,"stem":453},[515,516],{"title":456,"path":457,"stem":458},{"title":460,"path":461,"stem":462},1785825436192]