4. Quick review to Mathematical finance

Annuity

An annuity or also called payments (depending on the real situation)  is basically a constant payment for a period of time. Therefore instead to compound every annuity we use this formula because is quicker.

The 4 formulas that we need to mathematical finance

Loans

First these easy concepts:

Payments. It´s interest + principal. Its also called debt service. computed from this formula

Interest. The amount of interest from the outstanding balance. Outstanding balance*i

Principal. The amount paid of the "real" loan, without take into accounts the interest. Therefore is payment-i

Balance. It´s also called Outstanding balance. it´s the total debt that the borrower has to pay

There are 4 types of loans

1.Pure discount (zero coupon)= The principal repayment. The Loan is not amortized until the last year (N) and interest is also accrued until then. Basically you don´t pay anything( even interest) until the last period.

Example: I borrow $5000 at 4.25% in 3 years. How much is the interest?

5000*(1.0425)^3=5664

5664-5000= € 664

2. Interest-only ( bullet). The Loan is not amortized until the last year BUT you are paying interest every period.

Example: I borrow $5000 at 2.75% in 6 years. How much is the interest?

5000*2.75%=137.5

3. Constant-principal ( linear amortization): The Loan is amortized linearly over its life. It´s easy just divide the loan over the periods.

Example: If I borrow $100.000 for 20 years, how much is the principal.( look at that we don´t need the interest rate)

100.000/20 = € 5.000

4. Constant payment ( mortgage): The Loan is amortized through equal payments (Debt Service). However, the mix of Interest Payment and Principal repayment will change from year to year. Payment =( interest + Principal ). In theory the hardest one because you have to use this formula.

Example: If I borrow $100.000 for 20 years, at 5% how much are the payments

= €8.025