Annuities and sinking fund, are different from one another. When the fund credit happens for a specific reason, then it is called a sinking fund. Furthermore, an annuity is paying or receiving money, generally a fixed amount for a specific time period. The annuity formula and sinking fund formula will make the facts more clear.
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Sinking Fund
As mentioned earlier, whenever there is a fund credit for a specific purpose then it is called a sinking fund. The credits take place periodically and happen over a constant time period at a fixed rate of interest. Furthermore, at the end of every period, the calculation of interest takes place.
To calculate the size of the sinking fund, one can use the formula.
A = P.A (n,i)
Where,
A = Saving amount
P = Periodic payment
n = Period of payment
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Annuity
An annuity is something that we see happening even at our home. Most of the times, we see our parents paying up an amount on a regular basis. The amount remains the same mostly and the payment takes place either monthly or yearly.
Furthermore, for example: If you live in a rented house, then your parents are likely to pay the rent every month. Other examples include paying for insurance, house loan, vehicle loan, etc. In all of the cases, your parents pay an equal amount for each and every month. However, the time period between the payments may vary. It can either be one month or even a year.
Similarly, in some of the cases, people receive a constant amount of cash, for example, pension. This is where the annuity formula comes in picture. An annuity is nothing but a fixed sum of money that one receives or pays over a period for a fixed time. Generally, the annuity formula helps to understand the process.
Therefore, an annuity is nothing but a payment system that takes place periodically over some specified time period. Furthermore, a special version of annuity is known as the perpetuity. In perpetuity, there is an involvement of receipts that takes place for more than the usual time.
For an annuity, these are the features for more than one payment.
- For the whole span of annuity, the amount of money paid and received is likely to remain the same.
- Between two successive payments, the time interval must remain constant.
Types of Annuity
An annuity is of two types:
- Annuity Regular
- Annuity Due or Annuity Immediate.
I. Annuity Regular
In this type of annuity, first regular payment generally happens during the end of the first year. Here is a table that will explain it better.
| Year | Payments |
| 1 | 15,000 |
| 2 | 15,000 |
| 3 | 15,000 |
| 4 | 15,000 |
| 5 | 15,000 |
Therefore, from the table, we can conclude the fact that the very first payment happens by the end of the first year. Hence, it is an annuity regular.
II. Annuity Due or Annuity Immediate
In this type of annuity, the first payment is usually made in the start i.e. start of the annuity. This is called annuity immediate or annuity due. Here is a table to make things clear.
| Beginning Year | Payments |
| 1 | 50,000 |
| 2 | 50,000 |
| 3 | 50,000 |
| 4 | 50,000 |
| 5 | 50,000 |
Therefore, from the table, it is evident that the first payment is done at the start of the first year. Hence, we call such an annuity as an annuity due or annuity immediate.
Solved Examples on Annuity Formula
Sinking Fund
Example: Calculate the needed amount that must be invested every year so that the total amount sums up to Rs. 3,00,000 by the end of 10 years. The rate of interest is 10%, compounded annually.
Solution: Here, A = Rs. 3,00,000; n = 10; i = 0.1. We know that,
A = P.A (n,i)
3,00,000 = P.A(10, 0.1)
= P * 15.9374248
∴ P = 3,00,000/15.9374248
= Rs. 18,825.62
Note: You can also use the formula for future value of annuity regular to calculate the final amount.
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