# Algebra [newbie]

• Mar 11th 2010, 06:36 AM
jon80
Algebra [newbie]
I need help to understand how to work out the following formulae:

a. (€240k * Present Value Annuity(x%, 5 payments)) +
Annual Interest
(€4M * Present Value(x%, 5 periods))
Principal amount

Find x

b. €120,000 * Present Value Annuity (x%) = €309250
Annual Lease Payment Fair Value of asset

Find PVA (x%).
• Mar 11th 2010, 07:38 AM
bjhopper
algerbra
Quote:

Originally Posted by jon80
I need help to understand how to work out the following formulae:

a. (€240k * Present Value Annuity(x%, 5 payments)) +
Annual Interest
(€4M * Present Value(x%, 5 periods))
Principal amount

Find x

b. €120,000 * Present Value Annuity (x%) = €309250
Annual Lease Payment Fair Value of asset

Find PVA (x%).

bjh
• Mar 11th 2010, 09:58 AM
jon80
Quote:

Originally Posted by bjhopper
bjh

I can't figure out how to define my problem more clearly. Does it involve substitution?
• Mar 11th 2010, 12:04 PM
bjhopper
algebra
Quote:

Originally Posted by jon80
I need help to understand how to work out the following formulae:

a. (€240k * Present Value Annuity(x%, 5 payments)) +
Annual Interest
(€4M * Present Value(x%, 5 periods))
Principal amount

Find x

b. €120,000 * Present Value Annuity (x%) = €309250
Annual Lease Payment Fair Value of asset

Find PVA (x%).

for each annuity state each given given value. For example A one dollar payment each month at a given annual interest rate is worth how much today after 10 year

bjh
• Mar 11th 2010, 08:57 PM
jon80
Quote:

Originally Posted by bjhopper
for each annuity state each given given value. For example A one dollar payment each month at a given annual interest rate is worth how much today after 10 year
bjh

I figured out as much, but how do I carry out the substitution to find the value of x%?
• Mar 12th 2010, 05:45 AM
bjhopper
algebra
Quote:

Originally Posted by jon80
I figured out as much, but how do I carry out the substitution to find the value of x%?

If you have PVA, PMT, N PVA/PMT = the annuity factor for Npayments at interest i.This is unusual but interest could be found easily by using a factor table which shows factors as a function on N and i.Finding i appears quite complex otherwise.

PVA=present value of annuity
PMT= payments to be made over n periods @ an interest of i per period.
Annuity equations are available on line

bjh
• Mar 12th 2010, 06:45 AM
jon80
Quote:

Originally Posted by bjhopper
If you have PVA, PMT, N PVA/PMT = the annuity factor for Npayments at interest i.This is unusual but interest could be found easily by using a factor table which shows factors as a function on N and i.Finding i appears quite complex otherwise.

PVA=present value of annuity
PMT= payments to be made over n periods @ an interest of i per period.
Annuity equations are available on line

bjh

So how would I simplify this equation:

309250 = 120,000 * (((1 + i) ^ 3) - 1) / i)

Check: i should be 8%
1. http://en.wikipedia.org/wiki/Annuity_(finance_theory)
• Mar 12th 2010, 08:01 AM
bjhopper
algebra
[quote=jon80;473274]So how would I simplify this equation:

309250 = 120,000 * (((1 + i) ^ 3) - 1) / i)

Check: i should be 8%
1. Annuity (finance theory) - Wikipedia, the free encyclopedia[/quote

the annuity factor is 309250/120000=2.577 Using a period of 3 years the interest is indeed 8% but your annuity factor is not equal to this so your formula needs to be corrected

bjh
• Mar 12th 2010, 08:07 AM
jon80
[QUOTE=bjhopper;473301]
Quote:

Originally Posted by jon80
So how would I simplify this equation:

309250 = 120,000 * (((1 + i) ^ 3) - 1) / i)

Check: i should be 8%
1. Annuity (finance theory) - Wikipedia, the free encyclopedia[/quote

the annuity factor is 309250/120000=2.577 Using a period of 3 years the interest is indeed 8% but your annuity factor is not equal to this so your formula needs to be corrected

bjh

hmm...interesting, however that's what wikipedia says :)

So, (309250/120000 ) / 3 years = 0.86, so I'm missing something out or else the check figure is rounded up...
• Mar 12th 2010, 08:48 AM
Wilmer
Just an observation...
3 annual payments of 120000 at 8% annually = FV of 389568
389568 / 1.08^3 = PV of 309251.6385....

Your equation: 309250 = 120,000 * (((1 + i) ^ 3) - 1) / i)
Can be solved for i, but only numerically...or by iteration.