# Determine The Modified Duration Or Volatility Of A Growing Perpetuity.

Question 1

Question 2

Was Galileo part of the Italian Renaissance? Galileo: Galileo (1564-1642) was an Italian scientist who helped found observational astronomy and got into trouble with the Catholic Church after supposedly defaming the Pope in one of his works. This led to him being driven into house arrest, and there he stayed for the rest of his life.
Question 3

Were the Carthaginians in Sicily? Military Technology: The trireme was a war ship used by both the Romans and Carthaginians during the First Punic War. When the Romans figured out how to build triremes and use them, the balance of power in the war shifted to their favor.
Question 4

What did the Romans gain after defeating Carthage? Neighboring Powers: After the Punic Wars, the Romans became the most powerful state in the western Mediterranean. The series of wars was inevitable as the two powers in the region expanded up against each other.

Let us first determine Macaulay Durarion as

1v(1) + 2v^2(2) + 3v^3(3)…

Let us call Sum as S, and multiply by v, so we have

(1-v)S = v + 3v^2 + 5v^3…

Here v = (1+8%)^ (-1)

THe RHS of this equation can be solved using P,Q formula, or by arithemiatci sums to get Macaulay Duration as26.

Modified Duration – MacCaulay Duration x V

So, modified duration = 26/1.08 = 24.07 or 24 years