### Key Points of Financial Mathematics- Cashflow Models

1. Net Cashflow = Inflow - Outflow

2. Theory Viewpoint of Continuously Payable Cashflow = We say this thing when cashflows are paid
very Frequently. Ex= daily or weekly.
We do this because mathematics used to investigate these cashflows is sometimes become easier when we use continuous rather than at regular intervals.

3. Where there is uncertainty about Amount or Timing of Cashflows. An actuary can assign probabilities to both the amount and existence of cashflow.

Main difference between CT1 and CT5 is that we calculate Present value in CT1 because we assume that amount will definitely come, so we won't consider probability.
But in CT5 we calculate Expected Present Value because here probabilities are assigned with corresponding future cashflows too.

4. Zero Coupon Bond: When a Bond is issued at a discount and matures at Par Value. The difference between issue price and redemption price is the interest that an investor earns over the period of time.
This risk is usually neglegible for bonds issued by Government that's why they offer less return.
But when issued by companies having risk greater than that, then these companies offer higher returns on that type of bonds.

5. Index-Linked Security: Let's understand Real terms and Nominal Terms.
Real Terms is when we take into consideration Inflation and Nominal terms is when we won't consider inflation. For Ex = If inflation is 5% and investor got return of 9%. Then approximately Real return = 9-5 = 4%. and Nominal return is 9%.

So under index-linked security, cashflows are linked with inflation index that's why they are unknown cashflows for an investor after paying for known cashflow in the beginning by investor.

The main difference between index linked security and fixed interest security is that under Index linked security payments are known in real terms and under Fixed interest security payments are known in nominal terms.

Let's see an Example:
 Date 1/1/14 1/1/15 1/1/16 1/1/17 Index 100 105 108 113

Rate of Inflation during 2014 is (105/100)-1 = 5%
Rate of Inflation during 2015 is (108/105)-1 = 2.86%
Rate of Inflation during 2016 is (113/108)-1 = 4.63%.

Note: In reality, inflation index at the time of payment are not related to it due to delays in Calculating the index. It is also possible that investor receives amount of an index from earlier period.

6. Share buy-back: It will result in some investors have to sell their shares back to company. The remaining shareholders will subsequently own a greater percentage of company.

7. Interest Only Loan: A loan that is repayable by a series of interest payments followed by a return of initial Loan amount.

8. Repayment Loan (Mortgage): A Loan that is repayable by series of payments that partial repayment of Loan Capital in addition to interest Payments.
Capital Outstanding Proportion in payment made goes on increasing payment after and payment and Interest payment Portion in payment also goes on Decreasing after subsequent payments because the interest will keep on charging on remaining loan amount which is less than what will be the Previous year.

9. Annuity Certain:  It provides a series of regular payments in return of Sinngle Premium.