The amount (future value) of an ordinary annuity is given. Find the periodic payments.
A = $14,500, and the annuity earns 6% compounded monthly for 10 years.
To find the periodic payments of an ordinary annuity, you can use the formula for the future value of an ordinary annuity:
A = P * [(1 + r)^n - 1] / r
Where:
A represents the future value of the annuity (in this case, $14,500)
P represents the periodic payment
r represents the interest rate per period (6% / 12 = 0.005, since it's compounded monthly)
n represents the number of periods (10 years * 12 months = 120 months)
Now, let's plug in the given values into the formula and solve for P:
14,500 = P * [(1 + 0.005)^120 - 1] / 0.005
To make things simpler, let's break down the formula into steps:
Step 1: Calculate the value inside the square brackets:
(1 + 0.005)^120 = 1.790847
Step 2: Calculate the value inside the parentheses:
[1.790847 - 1] / 0.005 = 158.168038
Step 3: Solve for P:
14,500 = P * 158.168038
Dividing both sides of the equation by 158.168038:
P = 14,500 / 158.168038
Calculating this value:
P ≈ $91.79
Therefore, the periodic payment of the annuity is approximately $91.79.
P( (1+i)^n - 1)/i = amount
i = .06/12 = .005
n = 10(12) = 120
after all the others you did, I am sure you can take it from here.