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📈 Interest

An interest event represents a periodic interest payment from a debt instrument, fixed-income security, or lending arrangement.

📖 Definition

Interest is the cost of borrowing money, paid by the issuer (borrower) to the holder (lender). For investors, interest payments represent income earned from holding bonds, notes, term deposits, or peer-to-peer loans.

Unlike dividends (which depend on company profits), interest payments are contractually obligated — the issuer must pay the agreed rate regardless of financial performance.

Common interest schedules:

Frequency Typical Instruments
Monthly Savings accounts, P2P loans
Quarterly Corporate bonds, some government bonds
Semi-annually US Treasury bonds, many European government bonds
Annually Some corporate bonds, term deposits
At maturity Zero-coupon bonds, certificates of deposit

🧮 Interest Formulas

📏 Simple Interest

Interest calculated only on the original principal — no compounding:

\[ I = P \times r \times t \]

Where:

  • \(P\) = principal (initial investment)
  • \(r\) = annual interest rate (e.g., 0.04 for 4%)
  • \(t\) = time in years

Used for: short-term loans, some savings accounts, treasury bills.

📈 Compound Interest

Interest calculated on principal plus previously accumulated interest:

\[ A = P \times \left(1 + \frac{r}{n}\right)^{n \times t} \]

Where:

  • \(A\) = final amount (principal + interest)
  • \(P\) = principal
  • \(r\) = annual interest rate
  • \(n\) = compounding frequency per year (12 = monthly, 4 = quarterly, 1 = annual)
  • \(t\) = time in years

The interest earned is: \(I = A - P\)

Used for: most bonds, savings accounts with reinvestment, P2P platforms.

📉 Impact on Market Price

For coupon-bearing bonds, interest payments cause a periodic reset of the accrued interest component:

  1. Between coupon dates, the bond's "dirty price" (clean price + accrued interest) increases gradually
  2. On the coupon payment date, the accrued interest resets to zero
  3. The clean price may dip slightly around the ex-coupon date
Bond coupon cycle

A bond with face value €1,000 pays a 4% annual coupon semi-annually (€20 every 6 months).

  • Day before coupon: Clean price €980, Accrued interest €20 → Dirty price €1,000
  • Coupon date: Accrued interest resets to €0, investor receives €20 cash
  • Day after coupon: Clean price €980, Accrued interest ≈ €0.11 → Dirty price €980.11

For Scheduled Investment assets in LibreFolio, interest events directly modify the calculated price:

\[ \text{price}(d) = V_0 + I_{accrued}(d) - \sum_{k} C_k \]

Where:

  • \(V_0\) = initial investment value
  • \(I_{accrued}(d)\) = interest accrued up to date \(d\)
  • \(\sum_k C_k\) = sum of all interest payments (coupons) already distributed

📊 Yield Metrics

📐 Current Yield

The simplest yield measure — annual income relative to current price:

\[ \text{Current Yield} = \frac{\text{Annual Coupon}}{\text{Current Market Price}} \times 100 \]

Where:

  • Annual Coupon = total coupon payments per year (e.g., €40 for a 4% bond with €1,000 face value)
  • Current Market Price = what you'd pay to buy the bond today

Limitation: ignores capital gain/loss if held to maturity.

📐 Yield to Maturity (YTM)

The total return anticipated if the bond is held until maturity, accounting for all cash flows: coupon payments, face value repayment, and the difference between purchase price and par value.

YTM is the rate \(y\) that satisfies:

\[ P = \sum_{t=1}^{T} \frac{C}{(1+y)^t} + \frac{F}{(1+y)^T} \]

Where:

  • \(P\) = current market price
  • \(C\) = coupon payment per period
  • \(F\) = face value (returned at maturity)
  • \(T\) = number of periods to maturity
  • \(y\) = yield to maturity (per period)

YTM must be solved numerically (no closed-form solution).

🧮 How LibreFolio Handles Interest

In LibreFolio, an INTEREST event is recorded with:

  • Date: The interest payment date
  • Amount: The cash amount received
  • Currency: The currency of payment

For Scheduled Investment provider assets, interest events are generated automatically from the configured interest schedule and directly affect the price calculation. For market-priced bonds, they serve as informational markers.