find the value of annuity for a 1=$3000, I=0.09, n= 25
To find the value of an annuity, you can use the formula:
A = P * (1 - (1 + r)^(-n)) / r
where:
A = Value of the annuity
P = Payment per period
r = Interest rate per period
n = Number of periods
In this case, the payment per period (P) is $3000, the interest rate per period (r) is 0.09, and the number of periods (n) is 25.
Now we can substitute these values into the formula:
A = 3000 * (1 - (1 + 0.09)^(-25)) / 0.09
To calculate this, we need to solve the expression inside the parentheses first and then divide it by 0.09:
A = 3000 * (1 - (1.09)^(-25)) / 0.09
Now, let's calculate (1.09)^(-25):
(1.09)^(-25) ≈ 0.208
(Note: rounded to 3 decimal places)
Now let's substitute this value back into the formula:
A = 3000 * (1 - 0.208) / 0.09
Simplifying further:
A = 3000 * 0.792 / 0.09
A ≈ $26,400
Therefore, the value of the annuity is approximately $26,400.