The amount (future value) of an ordinary annuity is given. Find the periodic payments.
A = $2500, and the annuity earns 6.5% compounded annually for 4 years.
solve for P
P( 1.065^4 - 1)/.065 = 2500
didn't get it right, the answer in the book is 567.26
I got 567.26
P( 1.065^4 - 1)/.065 = 2500
P( 1.286466351 - 1)/.065 = 2500
P(.286466...)/.065 = 2500
P(4.40717...) = 2500
P = 2500/4.40717.. = 567.256
yeah you are right i just plug it in wrong , thanks soooo much!
To find the periodic payments of an ordinary annuity, we need to use the formula for the future value of an ordinary annuity:
A = P * [(1 + r)^n - 1] / r
where:
A = future value of the annuity
P = periodic payment (what we want to find)
r = interest rate per period
n = number of periods
In this case, we are given:
A = $2500
r = 6.5% = 0.065 (converted to decimal)
n = 4
We can plug in these values into the formula and solve for P:
$2500 = P * [(1 + 0.065)^4 - 1] / 0.065
To isolate P, we can first multiply both sides of the equation by 0.065:
$2500 * 0.065 = P * [(1 + 0.065)^4 - 1]
Simplifying further:
$162.50 = P * (1.065^4 - 1)
Now, let's calculate (1.065^4 - 1):
(1.065^4 - 1) = 1.30236
Substituting this back into the equation:
$162.50 = P * 1.30236
Finally, to solve for P, we divide both sides of the equation by 1.30236:
P = $162.50 / 1.30236
P ≈ $124.92
Therefore, the periodic payments of the annuity are approximately $124.92.