Problem 4 For a nominal interest of 6 per year what is the i

Problem 4, For a nominal interest of 6% per year, what is the interest rate if interest is: emectiveannual a. (5 pts) Compounded quarterly? b. (5 pts) Compounded Monthly? c. (5pts) Compounded yearly? d. (5 pts) Compounded continuously?

Solution

For non-continuous compounding,

Effective annual rate (EAR) = [1 + (r / N)]^N - 1, where

r: Nominal annual rate

N: Number of times compounding is done in a year

For continuous compounding,

Effective annual rate (EAR) = e^r - 1

(a) r = 6% = 0.06, N = 4

EAR = [1 + (0.06 / 4)]⁴ - 1 = (1 + 0.015)⁴ - 1 = (1.015)⁴ - 1 = 1.0614 - 1 = 0.0614 = 6.14%

(b) r = 6% = 0.06, N = 12

EAR = [1 + (0.06 / 12)]¹² - 1 = (1 + 0.005)¹² - 1 = (1.005)¹² - 1 = 1.0617 - 1 = 0.0617 = 6.17%

(c) r = 6% = 0.06, N = 1

EAR = [1 + (0.06 / 1)]¹ - 1 = (1 + 0.06)¹ - 1 = (1.06)¹ - 1 = 1.06 - 1 = 0.060 = 6.00%

(d) r = 6% = 0.06

EAR = e^0.06 - 1 = 1.0618 - 1 = 0.0618 = 6.18%