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# Breakthrough of Financing problems: Annuities and Perpetuities

Financing is one of the most attractive ideas that can be discussed today. There are various financial tools that financial managers from across the globes use in order to help in the decision making of a project. For the head start, consider Payback period, where we write the future cash flows from a project and determine in how much time it will be paid back. Another method, which can be seen as an improved version of payback period, is the NPV, where the time value of money is considered. This concept states that when predicting future cash flows and letting them adjust against an amount of money that will be spent today, it is important to consider the loss of value of money, e.g. due to inflation. Suppose someone tells you that you can make an investment today and you will be paid back every year. If they say that the payment will be fixed and paid for eternity, then that is called Perpetuity. English bonds are one example which was supposed to payback for as long as you owned the bond. If the value of the cash flow is going to increase, we call it growing perpetuity. This is an entirely separate concept (although very similar) and they both are calculated slightly differently. Now if you are told that the cash flow will be for a limited time, but it will be fixed, you get introduced to a new concept called annuity. By now, you would have followed, if this cash flow is going to be for a fixed amount of time but going to increase every year, you get growing annuity. The concept of annuity Is far more real and we have plenty of examples in the modern world. You can create a fixed deposit account for 5 years and It will pay you back every year, although the interest will be on the prime deposit, so it will be fixed.

It might seem unrealistic, but it is fairly easy to calculate the value of perpetuities and annuities.

• Present value of Perpetuity = C / r
• Present value of Growing Perpetuity = C/ r – g
• Present value of Annuity = C [1 – 1/(1+r)^t]/ r
• Present value of Growing Annuity = C [1-{ (1+g)/(1+r)}^t]/r-g

Where “C” represents the cash flows, “r” Represents the discounting rate and “g” represents growth rate.

To show you the capability of these concepts, consider that you have daughter who was just born today. You decide that you will send her to a good college when she turns 17 and will finance her yourself for 4 years of college. You want to know, that how much should you deposit in a bank every year, where the accumulated interest will let you reach your target? It is a fairly easy calculation, where you can simply calculate the present value of the total amount on her 17th birthday, and use the concept of Annuity to see how much cash flows you will need. The more one understands this concepts, the wider the range of uses. 