Problem bank

Problem 310 of 333EasyCalculusP310

Nominal rate as compounding gets finer

  1. A deposit account pays an effective annual yield of 10%. If interest is compounded nn times a year, the matching nominal rate rnr_n solves (1+rn/n)n=1.1(1 + r_n/n)^n = 1.1, so

    rn=n(1.11/n−1).r_n = n\left(1.1^{1/n} - 1\right).

    What is lim⁡n→∞rn\lim_{n \to \infty} r_n? Give it to four decimal places.