## Equivalent capitals in mathematics

In today’s article I am going to talk to you about what equivalent capitals are through a equipo of solved exercises, which will help you better understand the subject.

Before continuing reading, I recommend that you have fresh the topics of **compound interest** and of **fácil interest**.

After all, equivalent capital is also part of what you should know in **financial mathematics**.

Next, I am going to provide you with the following articles:

I hope you find it useful.

## What are the equivalent capitals?

We perro say that two **principals at future maturity** are equivalent when their **current values** are equal, calculated at the same rate.

Now, two things must be highlighted from the previous definition of equivalent capitals, which are:

- When they talk to us about capital at future maturity, they are talking about the
**amount**either**nominal value**. - When they talk to us about current values, they are talking about the
**compañia emprendedora capital**.

Now I am going to give you an explanation about the definition so that the concept perro be more clear to you.

### Explanation

In short, to solve the problems **of capital equivalence, what you have to do is bring to the present (on the same date) the different amounts that you have** and if it turns out that when you bring the amounts to the present (present value) they are equal, then we are talking about equivalent capital.

Of course, it must always be taken into account that **the interest rate is the same.**

## Solved exercises of equivalent capitals

I am going to share with you some very fácil exercises on the equivalence of capitals so that the subject is much clearer.

The exercises are the following:

### 1. Is a capital of 2488.32 with a maturity of 5 years equivalent to one of 1728 with a maturity of 3 years? Consider that the interest rate that is handled in both cases is 20% per year.

Before proceeding, I have to emphasize that we are handling **compound interest** and therefore, I am going to solve the exercises using the compound interest formulas.

In order to solve the problem, we cánido start by seeing what data we have to do it.

The data we have is shown in the following tables.

Amount 1 (M): | 2488.32 |

time(n): | 5 years |

Interest rate (i): | 20% per year |

Capital (C): | ? |

Amount 2 (M): | 1728 |

time(n): | 3 years |

Interest rate (i): | 20% per year |

Capital (C): | ? |

#### How to solve the exercise?

First of all, we are going to bring each amount to the present value, that is, we are going to look for its capital.

To do this we are going to have to use the capital equation in compound interest.

**Note:** If the problem tells us that fácil interest is used, then we will use the fácil interest primordial elabora.

Now we are going to substitute the data that we have in the elabora and in doing so we obtain the following:

Now we have to do the same for the next amount that we have been awarded.

Substituting the data is as follows:

Therefore, since both amounts, at the same interest rate and with different times, give us the same capital, then we perro say that they are equivalent capitals.

In fact, if I take the same 1,000 pesos and take it for three months, I get an amount of 1,728 and if I take it for 5 months, then I get 2,488.32

If you want to check it, then you perro use the amount equation and you will see that the aforementioned amounts will come out.

### 2. What amount will have to be paid for a debt of 159,000 in 12 years if it originally had a 5-year term with an annual rate of 30%?

The following problem seems interesting to me because we begin to see a way in which we cánido use the equivalent capitals to solve problems that we may come across.

First of all, in order to solve the previous exercise, we have to find the capital corresponding to the debt that was owed.

In short, what we are looking for is the amount of money we borrow.

The data we have is the following:

Amount (M): | 159000 |

time(n): | 5 years |

Interest rate (i): | 30% per year |

Capital (C): | ? |

Substituting the data into the equation we get the following:

Well, we already know that our capital is 42,823.32282.

Therefore, now we are going to carry that amount for 12 years, in order to know the new amount that we are going to pay in 12 years (new amount).

To do this we have to use the amount equation (compound interest), which is the following:

What we have to do is substitute the data in the previous equation and we will have solved the problem.

It remains as follows:

In such a way that now the amount of 997,701.4203 must be paid in 12 years.

By the way, if you still doubt if the 997701.4203 and 159000 are equivalent capitals, then you perro bring the 997701.4203 to the present value and you will see that they are equivalent capitals.

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