# Annuity overdue

The overdue annuity is that frequent payment, withdrawal or deposit that is made at the end of each agreed payment period.

In other words, an overdue annuity is one that is paid every end of the month, semester or year, for example.

A case of past due annuity could be the pensions that must be paid for the monthly payment of the university. Another example is the fees generated by a mortgage loan.

It should be remembered that an annuity is an income or outlay of money that takes place every certain interval of time, which should not always be a year.

## Items of Overdue Annuities

The elements of annuities are:

- Rent: Amount withdrawn, deposited or paid periodically.
- Rent payment period: Time interval established between one rent and another.
- Term of the annuity: Period that elapses between the first and the last income.
- Annuity rate: Interest rate set for the operation. For example, as in the case of a loan, where each installment will incorporate the accrued interest.

## Expired annuity example

As we mentioned, an example of a past due annuity is the installments of a loan. Let's imagine that these are installments of 1,500 euros that will be paid monthly for 18 months. So, we can calculate the future value, that is, the accumulated amount of payments at the end of the annuity term, with the following formula:

Where:

VF = Final value.

R = Income.

n = Number of payments.

i = Interest rate per compounding period.

So, assuming that the monthly interest rate, compounded monthly, is 3%, we would have:

Likewise, we can calculate the Present Value (PV) of the same loan with the following formula:

Therefore, we have:

This figure is the result of discounting towards period 0 all future payments. It is similar to the calculation of the net present value (NPV), only that in the latter case a project with an initial investment is usually being evaluated. Instead, annuities are simply a series of future payments.

It should be noted that the formulas presented are not applicable if the income is irregular or not constant.