Prime Brokers in Investment Banking
Investment banks all over the world have deep relationships with hedge funds. This is because investment banks often become the source of funds for the highly leveraged investments which are made by hedge funds. These funds are often made available through an organization called a prime broker. It needs to be understood that most prime […]
Cashless Economy: Pros and Cons
Governments across the world have stepped up their fight against cash. Cash is being increasingly viewed as a curse that mankind needs to rid itself of. The goal is to move towards a cashless economy. The closer an economy is towards this goal, the more successful it is considered to be. However, the concept of […]
The Harshad Mehta Scam in India (1992)
Harshad Mehta was the son of a peon. He was born in abject poverty and when he migrated to Mumbai, he had a mere Rs 40 i.e. less than $1 in his pocket. However, over the years Harshad Mehta rose meteorically to become one of the most influential and powerful brokers on the Bombay Stock […]
Misconceptions about Personal Finance
The importance of financial planning at an individual and family level cannot be overstated. For years, people and even governments have been trying to inculcate this habit into the masses. However, they have found it difficult to do so. This is because there are several misconceptions related to personal finance, which are common among people. […]
The Anatomy of Commodity Indices
Movements in the stock markets are easy to track. This is because instead of looking at the movements in the price of several different stocks, investors can simply look at the movement in the underlying index. This is where the concept of index is derived from. It provides a pulse of the market wherein one […]
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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