by Determining present value and Future value of annuity stream of payments
The present value and future value of an annuity stream of payments can be calculated using the following formulas:
Present Value of an Annuity:
PV = PMT x ((1 – (1 + r) ^ (-n)) / r)
Where:
PV = Present value of the annuity
PMT = Payment amount per period
r = Interest rate per period
n = Number of periods
Future Value of an Annuity:
FV = PMT x (((1 + r) ^ n) – 1) / r
Where:
FV = Future value of the annuity
PMT = Payment amount per period
r = Interest rate per period
n = Number of periods
Here’s an example to illustrate how to calculate the present value and future value of an annuity stream of payments:
Example:
Suppose you plan to receive an annuity stream of payments of $10,000 per year for the next 5 years, and the interest rate is 6% per year. You want to calculate the present value and future value of this annuity stream of payments.
To calculate the present value of the annuity, we use the present value formula:
PV = PMT x ((1 – (1 + r) ^ (-n)) / r)
Where
PV is the present value
PMT is the payment amount per period
r is the interest rate per period
n is the number of periods.
Plugging in the numbers we get:
PV = $10,000 x ((1 – (1 + 6%) ^ (-5)) / 6%)
PV = $40,225.38
Therefore, the present value of the annuity stream of payments is $40,225.38.
To calculate the future value of the annuity, we use the future value formula:
FV = PMT x (((1 + r) ^ n) – 1) / r
Where
FV is the future value
PMT is the payment amount per period
r is the interest rate per period
n is the number of periods.
Plugging in the numbers we get:
FV = $10,000 x (((1 + 6%) ^ 5) – 1) / 6%
FV = $63,404.51
Therefore, the future value of the annuity stream of payments is $63,404.51.
Compounding frequency, The present value of perpetuities
Compounding frequency refers to the number of times per year that interest is added to the principal amount in a savings account, investment, or loan. The more frequently interest is compounded, the higher the effective interest rate will be. For example, if a savings account compounds interest monthly, the effective annual interest rate will be higher than if the account compounds interest only once per year.
The present value of perpetuities is a financial calculation used to determine the present value of a series of payments that are made indefinitely, with no end date. A perpetuity is often used to describe a bond or other investment that pays a fixed amount of interest each year, with no maturity date.
The formula for calculating the present value of perpetuities is:
PV = PMT / r
Where:
PV = Present value of the perpetuity
PMT = Payment amount per period
r = Interest rate per period
Here’s an example to illustrate how to calculate the present value of perpetuities:
Example:
Suppose you have a perpetual bond that pays $1,000 per year in interest, and the interest rate is 5%. You want to calculate the present value of this perpetuity.
To calculate the present value of the perpetuity, we use the present value formula for perpetuities:
PV = PMT / r
Where
PV is the present value
PMT is the payment amount per period
r is the interest rate per period.
Plugging in the numbers we get:
PV = $1,000 / 5%
PV = $20,000
Therefore, the present value of the perpetuity is $20,000.
In summary, the compounding frequency refers to the number of times per year that interest is added to the principal amount in an investment or loan, and the present value of perpetuities is a financial calculation used to determine the present value of a series of payments that are made indefinitely. The present value of perpetuities can be calculated using the present value formula for perpetuities, which involves the payment amount per period and the interest rate per period.
