A sum of $50,000 is invested at a rate R, selected from a uniform distribution on the interval (0.03, 0.07). Once R is selected, the sum is compounded instantaneously for a year, so that X = 50000 eR dollars is the amount at the end of that year.

(a) Find the cdf and pdf of X.

(b) Verify that X = 50000 eR is defined correctly if the compounding is done instantaneously. Hint: Divide the year into n equal parts, calculate the value of the amount at the end of each part, and then take the limit as n→∞.

Physics Electricity and Magnetism (Professor Perdekamp) : Week 1 Notes Prelecture: Coulomb’s Law ...