My Math Forum Present Value Annuity Problem

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 May 29th, 2015, 08:41 AM #1 Newbie   Joined: May 2015 From: Italy Posts: 3 Thanks: 0 Present Value Annuity Problem Please could someone help me on this one? Consider an annuity with maturity after 8 years that is continuous with semestral density a=50 euros in the first 2 years and discrete with annual payments of 100 euros in the following period. Compute the present value of the annuity. (compound convention, annual rate i=10%). Thank you in advance!
 May 30th, 2015, 12:36 AM #2 Member     Joined: May 2014 From: Rawalpindi, Punjab Posts: 69 Thanks: 5 i=10% p_a = 1/2 = 0.5 c_a = 0 n_a = 4 aey(i, c_a) = e^i - 1 aey(10%, 0) = e^(10%) - 1 aey(10%, 0) = e^(0.1) - 1 aey(10%, 0) = 2.718282^(0.1) - 1 aey(10%, 0) = 1.105171 - 1 aey(10%, 0) = 0.105171 aey(10%, 0) = 10.52% x_a = [1 + aey(i, c_a)]^(p_a) x_a = (1 + 10.52%)^(0.5) x_a = (1.1052)^(0.5) x_a = 1.051271 i=10% p_d = 1 c_d = 1 n_d = 6 aey(i, c_d) = (1+i*c)^(1/c) - 1 aey(10%, 1) = (1+10%/1)^(1) - 1 aey(10%, 1) = (1.1)^(1) - 1 aey(10%, 1) = 1.1 - 1 aey(10%, 1) = 0.1 aey(10%, 1) = 10% x_d = [1 + aey(i, c_d)]^(p_d) x_d = (1 + 10%)^(1) x_d = (1.1)^(1) x_d = 1.1 PV = 50 * [1 - (x_a)^(-n_a)] / [x_a - 1] + 100 * (x_a)^(-4) * [1 - (x_d)^(-n_d)] / [x_d - 1] PV = 50 * [1 - (1.051271)^(-4)] / [1.051271 - 1] + 100 * (1.051271)^(-4) * [1 - (1.1)^(-6)] / [1.1 - 1] PV = 50 * (1 - 0.818731) / 0.051271 + 100 * (0.818731) * (1 - 0.5644739) / 0.1 PV = 50 * 0.18126925 / 0.051271 + 100 * (0.818731) * 0.4355261 / 0.1 PV = 50 * 3.53551 + 100 * (0.818731) * 4.355261 PV = 176.77 + 100 * 3.5657859 PV = 176.77 + 356.58 PV = 533.35 Thanks from Anna
 May 30th, 2015, 01:10 PM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 The "continuous" is unclear...assuming it does not mean "interest compounding continuously", and that the interest is 10% EFFECTIVE annually: i = 1.1^(1/2) - 1 = .04888... u = FV of the semi-annual portion. u = 50[(1+i)^4 - 1] / i = 215.12492... i = .10 u = u(1+i)^6 = 381.10693... v = FV of the annual portion. v = 100[(1+i)^6 - 1] / i = 771.5600... PV = (u + v) / (1 + i)^8 = 537.7281... Have I been inspired by the Hoooooly Spook, Dexter? Thanks from Anna
May 30th, 2015, 07:38 PM   #4
Member

Joined: May 2014
From: Rawalpindi, Punjab

Posts: 69
Thanks: 5

Quote:
 Originally Posted by Denis Have I been inspired by the Hoooooly Spook, Dexter?
I didn't know what it meant till I looked it up in a dictionary

spook (spo͞ok)

n.
1. Informal A ghost; a specter.
2. Slang A secret agent; a spy.
3. Offensive Slang Used as a disparaging term for a black person.
v. spooked, spook·ing, spooks
v.tr.
1. To haunt.
2. To startle and cause nervous activity in; frighten: The news spooked investors, and stock prices fell.
v.intr.
To become frightened and nervous.

 May 30th, 2015, 07:42 PM #5 Member     Joined: May 2014 From: Rawalpindi, Punjab Posts: 69 Thanks: 5 All of the above
 May 30th, 2015, 09:23 PM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 I used holy spook = holy spirit, the 3rd member of the holy trinity. Bow your head in reverence. In the name of Big Daddy, of Sonny Boy, and of The Holy Spook. Hahmen! Be advised that it is the Holy Spook who inspires the Pope. Father and Sonny are too busy handling their real estate business.
 May 31st, 2015, 10:07 AM #7 Newbie   Joined: May 2015 From: Italy Posts: 3 Thanks: 0 Thank you both for your help!

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