Question

Annuity Period - As you increase the length of time involved, what happens to the present value of an annuity? What happens to the future value?

Please explain why

Answer 1

Annuity is a series of payment which is made or received in the future. Such payments can be against a loan/ mortgage or towards an investment plan.

If we increase the length of time involved, the number of payments become more. For example consider an annuity of $800 for 8 years. This annuity will have a certain present value which can be calculated with the help of interest rate involved. Now suppose we increase the time period by 1 years and make the total period to be 9 years, the number of payments will increase by (9-8) = 1 years. This means one more payment of $800, which will be discounted at $800/ (1+x%)^9.

Thus, when the annuity length is increase the present value increase. Same is the case wil Future value. Lets take the same example of $800 for 8 years, this time invested at a certain rate. If the length is increased by 1 more year, the whole annuity will remain invested for 1 more years, i.e. 9 years instead of 8 years. Also, one additional investment of $800 will be added, further increasing the Future value.

Thus, due to the concept of compuding and time value of money, the Present value as well as the future value of the annuity increases.