📚 How Plan 5 Student Loan Interest Is Calculated and Added to Your Account | 第五类还款计划学生贷款利息如何计算并计入账户
Plan 5 is the student loan repayment plan used for undergraduate loans in England for courses starting on or after 1 August 2023. Unlike a normal bank loan, the interest is not charged as a single yearly figure on a fixed sum. Instead, it is calculated every single day on whatever balance is outstanding, and then added to your account at the end of each month. Understanding that two-step mechanism - daily accrual, monthly capitalisation - is the key to predicting how your balance will move over forty years.
第五类还款计划（Plan 5）适用于2023年8月1日及以后开课的英格兰本科学生贷款。与普通银行贷款不同，它的利息并不是按固定本金每年一次性计算，而是每天按当日未偿余额逐日计提，再在每月月末计入账户。理解"按日计提、按月资本化"这两个步骤，是预测你未来四十年余额变化的关键。
1. What Plan 5 Is and Who It Applies To | 什么是第五类还款计划及其适用对象
Plan 5 replaced Plan 2 for new English undergraduate borrowers. It is not a mortgage-style loan with a fixed term and fixed instalments; it behaves much more like a graduate contribution. Repayment depends on your income, not on how much you borrowed, and any balance left after the write-off period simply disappears.
第五类计划取代了原有的第二类计划（Plan 2），适用于英格兰新的本科借款人。它并不是期限固定、每期还款额固定的按揭式贷款，而更像一种"毕业生贡献金"。还款额取决于你的收入，而不是你借了多少；核销期结束后剩余的余额会自动取消。
The four defining parameters are the repayment threshold, the repayment rate, the write-off period and the interest rate. These four numbers, together with your salary, determine everything.
决定一切的是四个核心参数：还款门槛、还款比例、核销期限和利率。这四个数字加上你的薪资，就决定了全部结果。
| Parameter | 参数 | Plan 5 value | 第五类计划数值 |
| Repayment threshold | 还款门槛 | £25,000 per year (frozen to 2026-27, then uprated with average earnings) | 每年 £25,000（冻结至2026-27学年，之后随平均工资增长上调） |
| Repayment rate | 还款比例 | 9% of income above the threshold | 超过门槛部分的 9% |
| Write-off | 核销期限 | 40 years from the April after course end | 课程结束后次年4月起算的40年 |
| Interest rate | 利率 | RPI, set annually, never below 0% | 与RPI挂钩，每年公布，不会低于0% |
Note that Scotland, Wales and Northern Ireland operate separate arrangements, and postgraduate loans sit on different plans. Always confirm your plan from the letter or online account issued by the Student Loans Company (SLC).
注意：苏格兰、威尔士和北爱尔兰有各自的制度，研究生贷款也属于不同的还款计划。请务必以学生贷款公司（SLC）发给你的信函或在线账户信息确认自己属于哪一类计划。
2. The Interest Rate: How It Is Set Each Year | 利率：每年如何确定
Under Plan 5 the interest rate is set once a year and normally equals the Retail Prices Index (RPI) measured in the preceding March. The rate runs from 1 September to 31 August. Because it tracks an inflation index rather than a Bank of England base rate, it can move sharply: in a high-inflation year it has been well above commercial mortgage rates, and in a deflationary year it would be floored at 0% rather than turning negative.
第五类计划的利率每年确定一次，通常等于上一年3月公布的零售物价指数（RPI）。该利率适用于当年9月1日至次年8月31日。由于它挂钩通胀指数而非英国央行基准利率，波动可能很剧烈：高通胀年份可能远高于商业按揭利率；而在通缩年份，利率会以0%为下限，不会变成负数。
Two consequences follow. First, you must use the rate that applied in each specific period - you cannot simply apply today's rate across a 40-year projection. Second, the rate applies from the day the first payment reaches your account, which means interest starts running while you are still studying and have no income at all.
由此产生两个结果。第一，你必须按"每个时期当时适用的利率"分段计算，不能拿今天的利率去套四十年的预测。第二，利率从第一笔贷款到账之日就开始生效——也就是说，你还在读书、完全没有收入的时候，利息已在累积。
Always check the current published rate on the official government page before doing any calculation, and record the rate you used alongside any projection so the model can be updated later.
进行任何计算前，请先在官方政府页面上核对当期公布的利率；并在你的预测模型旁注明所用利率，以便日后更新。
3. Daily Accrual and Monthly Capitalisation | 按日计提与按月资本化
The single most misunderstood point is that interest is calculated daily but added monthly. Each day, SLC multiplies the outstanding balance by the annual rate and divides by 365 (or 366 in a leap year). That daily figure is not immediately added to your loan; it accumulates, and at the end of the calendar month the whole month's interest is posted to the account and becomes part of the balance.
最容易被误解的一点是：利息"按日计算、按月入账"。每天，SLC用当日未偿余额乘以年利率，再除以365（闰年为366）。这个日息并不会立刻加到贷款上，而是先累积；到自然月月末，当月全部利息一次性计入账户，成为余额的一部分。
Once interest has been capitalised, it itself starts earning interest the following day. This is compounding, and it is the reason a small rate difference produces a very large difference over 40 years.
一旦利息被资本化，它从次日起也开始产生利息。这就是复利效应，也是"利率差一点点、四十年后差很多"的原因。
Daily interest = Balance × Annual rate ÷ 365
Monthly interest = Balance × Annual rate ÷ 365 × Days in the month
Because months have 28 to 31 days, the monthly interest charge is not constant even when the balance is constant. A February posting is roughly 10% smaller than a January posting.
由于每个月有28至31天不等，即使余额不变，每月利息也不是固定值。2月的入账金额大约比1月少10%。
4. The Core Formula with Worked Examples | 核心公式与计算实例
Suppose your balance on 1 September is £45,000 and the rate for the year has just been set at 4.3%. Working through the daily figure first keeps the arithmetic transparent.
假设9月1日你的余额为 £45,000，新公布的当年利率为 4.3%。先算出日息，整个计算过程会非常清晰。
Annual interest = 45,000 × 0.043 = £1,935
Daily interest = 1,935 ÷ 365 = £5.301
30-day month = 5.301 × 30 = £159.04
Read that last figure carefully. The account grows by about £159 in a single month, without you receiving any money at all. Over a year the balance rises to roughly £46,974, an increase of about £1,974 rather than the simple £1,935, because of monthly compounding.
请仔细看最后一个数字：一个月之内，账户余额凭空增长约 £159，而你并没有拿到任何现金。一年之后余额约为 £46,974，增加约 £1,974，而不是简单利息的 £1,935——多出来的部分就是按月复利的结果。
The effective annual rate, which is what actually matters for projections, is slightly higher than the nominal rate:
对于长期预测而言，真正重要的是"实际年利率"，它略高于名义利率：
Effective annual rate = (1 + 0.043 ÷ 365)³⁶⁵ − 1 ≈ 4.39%
For most purposes, however, using the nominal rate with monthly compounding gives an answer close enough for planning, and it is far easier to explain and to check.
不过在大多数情况下，用名义利率配合按月复利做规划已经足够接近，而且更容易解释和复核。
5. Building a Month-by-Month Balance Table | 构建逐月余额表
The cleanest way to see how interest enters the account is a five-column table. Column A is the month, B the opening balance, C the monthly interest, D the repayment deducted from your salary, and E the closing balance. Row by row, the closing balance of one month becomes the opening balance of the next.
要看清利息如何进入账户，最清楚的方法是做一张五列表格：A列为月份，B列为期初余额，C列为当月利息，D列为从工资中扣除的还款额，E列为期末余额。逐行往下，上月的期末余额就是下月的期初余额。
| Month | 月份 | Opening balance | 期初余额 | Interest | 利息 | Repayment | 还款 | Closing balance | 期末余额 |
| 1 | £45,000.00 | £159.04 | £37.50 | £45,121.54 |
| 2 | £45,121.54 | £159.47 | £37.50 | £45,243.51 |
| 3 | £45,243.51 | £159.90 | £37.50 | £45,365.91 |
The repayment of £37.50 corresponds to a salary of £30,000, since 9% of £5,000 divided by twelve months is £37.50. Notice that the interest is more than four times the repayment, so the balance rises every month.
表中 £37.50 的还款额对应年薪 £30,000：超过门槛的 £5,000 的9%，再除以12个月。可以看到，利息是还款额的四倍以上，因此余额每月都在上升。
6. Repayments versus Interest: Negative Amortisation | 还款与利息对比：负摊销
On a normal loan, amortisation means each payment reduces the balance. On a Plan 5 loan, the opposite often happens. When the monthly interest exceeds the monthly repayment, the balance grows, and this is called negative amortisation.
普通贷款中，"摊销"意味着每期还款都会减少余额。而在第五类计划中，情况往往相反：当每月利息大于每月还款额时，余额反而增加，这被称为"负摊销"。
Work through the arithmetic for a typical starting salary:
用一份典型的起薪算一算：
Repayment = 0.09 × (£30,000 − £25,000) = £450 per year = £37.50 per month
Interest on £45,000 at 4.3% ≈ £159 per month
Monthly shortfall = £159 − £37.50 = £121.50
This is not a failure of the system; it is a deliberate design feature. Plan 5 is structured so that lower and middle earners make small contributions while the balance continues to grow, and the eventual write-off absorbs the remainder. The consequence for planning is important: your monthly repayment is never "the amount you owe this month". It is simply 9% of the excess income.
这并不是制度失灵，而是有意设计。第五类计划的结构是：中低收入者只做少量贡献，余额继续增长，最终的核销会消化余下部分。这对个人规划的重要含义是：你每月的还款额从来不是"这个月你欠了多少"，而仅仅是"超过门槛收入的9%"。
7. Break-Even Income: When the Balance Stops Growing | 收支平衡收入：余额何时停止增长
There is a salary at which your repayment exactly equals your interest charge. Above it, the balance falls; below it, the balance rises. The formula is a simple rearrangement.
存在一个薪水水平，使你的还款额恰好等于利息。高于它，余额下降；低于它，余额上升。公式只是一个简单的移项。
Break-even income = Threshold + (Annual interest ÷ 0.09)
For a balance of £45,000 at 4.3%, the annual interest is £1,935, so the required excess income is 1,935 ÷ 0.09 = £21,500. Adding the £25,000 threshold gives a break-even salary of £46,500.
余额 £45,000、利率 4.3% 时，年利息为 £1,935，所需超过门槛
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