Question

A bank pays 10% nominal annual interest on special three-year certificates. What is the effective annual interest rate if interest is compounded
a. Every three months?
b. Daily?
c. Continuously?

Answer 1

a. Every three months

$r=(1+\frac{0.10}{4})^4-1\\ r=(1.025)^4-1\\ r=0.1038\\ r=10.38\%$

b. Daily

$r=(1+\frac{0.10}{365})^{365}-1\\ r=(1.0757)^{365}-1\\ r=0.0757\\ r=7.57\%$

c. Continuously

$r=e^{0.10}-1\\ r=1.1051-1\\ r=0.1501\\ r=1.501\%$