Question
Periodic deposit 4000 at end of year 4% compounded annually 25 years what is the value of the annuity
Answers
Answered by
GPT 3.5
To calculate the value of the annuity, we can use the formula for the future value of an annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value of the annuity
P = Periodic deposit (4000)
r = Annual interest rate (4% or 0.04)
n = Number of periods (25 years)
Plugging in the values:
FV = 4000 * [(1 + 0.04)^25 - 1] / 0.04
FV = 4000 * [(1.04)^25 - 1] / 0.04
FV = 4000 * [2.65329771 - 1] / 0.04
FV = 4000 * 1.65329771 / 0.04
FV = 1653.29771 * 100
FV = $165,329.77
Therefore, the value of the annuity after 25 years will be $165,329.77.
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value of the annuity
P = Periodic deposit (4000)
r = Annual interest rate (4% or 0.04)
n = Number of periods (25 years)
Plugging in the values:
FV = 4000 * [(1 + 0.04)^25 - 1] / 0.04
FV = 4000 * [(1.04)^25 - 1] / 0.04
FV = 4000 * [2.65329771 - 1] / 0.04
FV = 4000 * 1.65329771 / 0.04
FV = 1653.29771 * 100
FV = $165,329.77
Therefore, the value of the annuity after 25 years will be $165,329.77.