Anualidad Diferida - Clase 18 - Matemáticas Financieras

Hello, hello, hello. My name is Eduardo Aponte and we are going to study financial mathematics. Welcome. Deferred annuity. A deferred annuity is a set of equal payments made at equal time intervals, with the first payment beginning after the first period. Let's look at an example. [Music] A pizzeria wants to buy a new

oven with which they can increase their production. The oven company offers to pay for the oven on credit. There will be 20 quarterly payments of $3,000 starting within a year. If the interest rate is 3% quarterly, what is the cash value of the oven? In this case, the cash flow would be as

follows. We can see that the first payment is made after a year, that is, at the end of the fourth quarter. If we use the present value formula for an annuity, we would be bringing the cash flows to period 3. Therefore, we will have to bring that value to period zero, that is, to the

present. To do this, we will simply use the following formula, [Music] where BP is the present value, BP sub N is the value at period N and is the periodic interest rate due and N is the number of periods. In summary, to find the value of the installment of a deferred annuity, two steps are performed.

The first is to use the present value formula for an annuity seen in lesson 14. And the second is to bring the value found in the first step to present value using the formula BP = the value found over 1 the periodic interest rate due and this raised to the n. Performing the steps in the example

seen, we have that BP is equal to 3000, which is the value of the oven, multiplied by 1 + 0.03, which is equivalent to the rate of 3% quarterly raised to the power of 20, which is the number of quarterly payments there are . And this -1 over 0.03 which multiplies 1 + 0.03 raised to the 20th power.