# Annuity: Present Value

• Dec 12th 2009, 10:12 PM
F4LL3N
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)
=\$107,100.80

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.
• Dec 13th 2009, 06:22 AM
Wilmer
Quote:

Originally Posted by F4LL3N
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?

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)
=\$107,100.80

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)
Formula:
P = a[1 - 1/(1 + i)^n] / i

P = 7400[1 - 1/(1+.0325)^20] / .0325 = 107591.16
• Dec 13th 2009, 03:36 PM
F4LL3N
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.