Different Types of Annuity Calculations

In the articles on present value, we learnt that the value of a dollar today is not the same as it will be 10 years from now. Then, we came across annuities which are a powerful mechanism that ensure that the nominal value of the payments remain the same throughout the years whereas its internal components i.e. interest and principal keep on changing. Annuities, therefore give a very useful way to work with a schedule of payments. There are various types of payment schedules possible while working with an annuity. Here are some of the important types:

Lump Sum to Annuity Payments

Annuities can convert a lump sum payment today into a series of future cash flows which will have the exact same value as of today. This is useful in business because usually the outlays required have to be done immediately in a lump sum whereas the benefits arrive at a later date and they arrive in installments. Annuities therefore enable us to draw a comparison between these values and decide if they are beneficial to us.

Example: Assuming a 12% rate of return for the next 5 years, an annual payment of $27.74 has the same present value as a $100 payment today. So we can choose between making a $100 payment upfront or choose a 5 year annuity of $27.74

Annuity Payments to Lump Sum

The reverse of the above calculation is also true. Annuities help us to take a series of future equal payments that will be made at equal periodic intervals and come up with a lump sum present value that is equal to those payments. This too is very useful. Let’s say that you are scheduled to make mortgage payments for the next 5 years. But instead you choose to pay upfront and close the loan. What is the amount that you should pay to the lender? Annuity calculations will help us come up with that amount.

Example: Assuming a 14% interest rate for the next 5 years and an annual payment of $100, the present value of this stream of payments is $343.31

Partial Lump Sum

Now, in the above cases we were converting lump sums into equal payments or equal annuity payments into lump sums. Annuity calculations can be used to arrive at the calculation of the two as well. The payment maybe partially made in equal installments and partially paid in a lump sum. For instance, if you owed the bank $500, you could pay $200 upfront and convert the balance into an annuity.

Annuity calculations allow you to convert any lump sum or stream of cash flows into any other lump sum or stream of cash flows or a combination of both. These calculations form the backbone of finance and it is difficult to imagine the financial world without them.

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