## Present Value of Amortized Bonds
An amortized bond is one where the principal is repaid in equal instalments over the bond's life, rather than as a lump sum at maturity. Each period's cash flow = Principal instalment + Interest on the outstanding balance.
### Structure of Cash Flows
For a bond of ₹P amortized over n years at coupon rate r%:
```
Annual principal instalment = P / n
Interest in year t = r% × Outstanding balance at start of year t
Cash flow in year t = P/n + r% × Outstanding balance
```
Because the outstanding balance falls each year, the cash flows are declining — highest in year 1, lowest in year n.
### Present Value Calculation
An investor who demands a minimum return of `k%` will value the bond as:
```
PV = Σ [CF_t / (1+k)^t] for t = 1 to n
```
Since each year's cash flow is different, discount each year's cash flow individually.
### Investor vs Issuer perspective
- The issuer (company) pays based on the coupon rate
- The investor values the bond based on their required return
- If required return < coupon rate → PV > face value (bond is worth more than par)
- If required return > coupon rate → PV < face value