Problem 17E

Some banks now compound daily, but report only on a quarterly basis. It seems to us that it would be easier to compound every instant, for then a dollar invested at an annual rate of i for t years would be worth eti. [You might find it interesting to prove this statement by taking the limit of (1 + i/n)nt as n→∞.] If X is a random rate with pdf f (x) = ce −x, 0.04 < x < 0.08, find the pdf of the value of one dollar after three years invested at the rate of X.

Answer :

Step 1 of 3 :

Given, some banks now report only on a quarterly basis, but compound daily.

It can be easier to compound every instant, for then a dollar invested at an annual rate f i for t years would be worth e.

Rete bo deposit is X and period of deposit is 3 years.

Let X be a random rate with pdf f(x) = c , 0.04 < x < 0.08.

Y =

The claim is to find the pdf value of one dollar after three years invested at the rate of X.