Annuity: Present Value
I have absolutely no idea what I am doing. I study with OTEN (I work from home), so asking a teacher becomes a problem.
Here's the question:
A relative wills you an annuity paying $7400 per half-year for the next 10 years. If this money can earn 6.5% pa compounded half-yearly, what is the present value of this annuity?
I've been through numerous answers, but when I re-work through the answer it does not seem to add up. They seem to be unreasonably too high or too low. Right now, this is what I come up with:
r=0.065 / 2 = 0.033
N=M(1+r)^n-1 / r(1+r)^n
N=7400 (1+0.033)^20 – 1 / 0.033(1+0.033)^20
=7400(1.033^20-1) / (0.033x1.033^20)
That's based off similar example questions. That seems incredibly wrong. The previous way I did it, I skipped the second last line, and the answer seemed too high - this one seems too low!
Like I said, I'm basing all that on example questions. So I don't know why it looks so wrong.
Can you tell me what I'm doing wrong, and give me the right way to do it.
Answer is 107,591.16
Originally Posted by F4LL3N
Change your "r" to .065 / 2 =.0325 (very important)
So you basically are doing it right.
EASIER like this:
P = Present value ( ?)
a = annuity amount (7400)
n = number of periods (20)
i = periodic interest rate (.0325)
P = a[1 - 1/(1 + i)^n] / i
P = 7400[1 - 1/(1+.0325)^20] / .0325 = 107591.16
Oh, okay. Thanks. So it was only the rate I got wrong.
I thought my answer would have been 60,000 too low atleast. I guess I don't really understand it all yet.