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The Financial System and Basel Accords
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Annuities can be divided into two types based on the exact time when the payments occur in a given period. The payments could either occur at the beginning of every period or the payments could occur at the end of every period. For instance when you take a house on rent, the rent is usually paid in advance whereas when your mortgage payments are usually made at the end of every period. So the payments made at the end of every period are called ordinary annuity. This is because ordinary annuity is the usual state of affairs. Usually all annuities are paid at the end of the period.
Alternatively, when annuity payments are made in advance, we call them annuity due. The difference in the formula to calculate the two different types of annuities is very small. Also, the difference in amounts is not expected to be large either. However, to be precise, a student of finance must know the difference between ordinary annuity and annuity due and know when to use the formulas.
As we seen that ordinary annuity payments are made at the end of each period whereas the payments for annuity due are made at the beginning of each period. Hence, the difference between ordinary annuity and annuity due is one extra period. Thus, an adjustment needs to be made for this one extra period while calculating both the present value and future value of an annuity due.
Future Value of an Annuity Due: Let’s say that we want to calculate the future value of an annuity which pays $100 for 5 years and the payments begin at the beginning of the first period. The rate of interest is 10%
If we used the regular annuity formula or table, we would be given the future value of the above case as $610.51. However, this is the value if the payments were made at the end of each period. To convert them into annuity due we need to account for the one extra period. So we further multiply the answer by (1+i). In our case, since the interest rate is 10% per annum, we multiply it by 1.1. So the future value of the same example would be $610.51*(1.1). In this case the answer is $671.56
Calculating the present value of annuity due is a simple 2 step procedure:
Present Value of an Annuity Due: Let’s say that you were to receive 5 annual payments of $100 each for the next 5 years beginning at beginning of each period and your required rate of return is 10% per annum.
If we used the regular annuity formula or table, we would be given the present value of the above case as $379.08. However, this is the value if the payments were made at the end of each period. To convert them into annuity due we need to account for the one extra period. So we further divide the answer by (1+i). In our case, since the interest rate is 10% per annum, we divide it by 1.1. So the present value of the same example would be $379.08/(1.1). In this case the answer is $344.6.
Calculating the present value of annuity due is a simple 2 step procedure:
Please note the difference. While calculating future values, we compounded the result for an extra period i.e. we multiplied. On the other hand, while computing present values, we discounted for one extra period i.e. we divided the result.
The concept of annuity due will be hidden in the question i.e. it will not be explicitly stated. Hence, one must pay attention to when the payments are being made to determine whether it is an ordinary annuity or an annuity due.
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