My Math Forum  

Go Back   My Math Forum > Science Forums > Economics

Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance


Thanks Tree2Thanks
  • 1 Post By AbrahamA
  • 1 Post By Denis
Reply
 
LinkBack Thread Tools Display Modes
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!
Anna is offline  
 
May 30th, 2015, 12:36 AM   #2
Member
 
AbrahamA's Avatar
 
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
AbrahamA is offline  
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
Denis is offline  
May 30th, 2015, 07:38 PM   #4
Member
 
AbrahamA's Avatar
 
Joined: May 2014
From: Rawalpindi, Punjab

Posts: 69
Thanks: 5

Quote:
Originally Posted by Denis View Post
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.
AbrahamA is offline  
May 30th, 2015, 07:42 PM   #5
Member
 
AbrahamA's Avatar
 
Joined: May 2014
From: Rawalpindi, Punjab

Posts: 69
Thanks: 5

All of the above
AbrahamA is offline  
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.
Denis is offline  
May 31st, 2015, 10:07 AM   #7
Newbie
 
Joined: May 2015
From: Italy

Posts: 3
Thanks: 0

Thank you both for your help!
Anna is offline  
Reply

  My Math Forum > Science Forums > Economics

Tags
annuity, present, present value, problem



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
present value/linear programming problem jtmalu2 Economics 0 October 24th, 2011 08:14 PM
Annuity problem! ik2244 Calculus 1 December 3rd, 2010 09:02 AM
Annuity Problem tbl9301 Economics 3 September 16th, 2009 07:10 AM
Present value annuity tbl9301 Economics 2 September 8th, 2009 02:54 PM
Present Value of An Annuity simplequestion Economics 3 October 8th, 2008 12:41 PM





Copyright © 2019 My Math Forum. All rights reserved.