yield calculation

[Vinay Naga]

I have a Mathematical equation that cannot be solved linearly. Can some one help me find a simple logic to calculate yield.

Given a financial instrument which offers the annual payments

Years from NowPromised Annual Payments
1$2,000=c1
2$2,000=c2
3$2,500=c3
4$4,000=c4

The price of the financial instrument is :$7,704=P
Use the equation below to calculate the yield y:

P = (c1/((1+y)^1)) + (c2/((1+y)^2)) + (c3/((1+y)^3)) + (c4/((1+y)^4))
where P, c1, c2, c3, and c4 are above
and y is the yield of the financial instrument

Find the yield y which satisfies the above equation.

Write a JAVA console or windows program to do this.
Input :
input for c1
input for c2
input for c3
input for c4
input for price

Output:
yield y

There has to be a way to start from the approx. value. I need some advice on this.

Thanks for your help,
Vinay

[Rob Spoor]

This is not a Java problem per se, but just a mathematical problem.

You have an equation with only one variable - y. You will have to rewrite that to make it easier. For instance:

P == (c1/((1+y)^1)) + (c2/((1+y)^2)) + (c3/((1+y)^3)) + (c4/((1+y)^4))
=== // multiple both sides with (1+y)^1, (1+y)^2, (1+y)^3 and (1+y)^4, under the assumption that y != -1
P * (1+y)^1 * (1+y)^2 * (1+y)^3 * (1+y)^4 == c1 * (1+y)^2 * (1+y)^2 * (1+y)^3 + c2 * (1+y)^1 * (1+y)^3 * (1+y)^4 + c3 * (1+y)^1 * (1+y)^2 * (1+y)^4 + c4 * (1+y)^1 * (1+y)^2 * (1+y)^3

Now rewrite that into a form of a * y^4 + b * y^3 + c * y^2 + d * y + e == 0, and solve that.

However, this is not the place for that. Moving to a more appropriate forum.

[Jesper de Jong]

That last equation is a quartic equation. (Follow the link for more info on solving it).

[Gabriel Claramunt]

Maybe there's a numerical method to solve it...

[Jesper de Jong]

You could find an approximate solution with a numerical method, but quartic equations can also be solved algebraically, as is explained on the Wikipedia page that I posted a link to.