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Some banks now compound daily, but report only on a
Chapter 3, Problem 17E(choose chapter or problem)
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.
Questions & Answers
QUESTION:
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:
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.