Question

Find the interest rates in the following situations. 

a. APR-9%, compounded monthly. Find the effective annual interest rate. 

b. Nominal rate is 7% compounded quarterly. Find the effective semi-annual rate. 

c. The effective annual interest rate is 17.41% and compounding is monthly. Find the nominal interest rate. 

d. r = 5% and compounding is monthly. Find the effective quarterly interest rate. 

a. The effective annual interest rate is 9.4 %. (Round to one decimal place.)

b. The effective semi-annual rate is _______  %. (Round to one decimal place.)

Answer 1

Nominal rate = > r = 7 % = 0.07 N = quarterly = 4 Re = [(1 + (R/N))^N - 1] times 100 Re = [(1 + (0.07/4))^4 - 1] times 100 = ((1 + 0.0175)^4 - 1) 100 = ((1.0175)^4 - 1) 100 = (1.0718 - 1) 100 = 7.18 % Effective semiannual rate r = [(1 + Re)^1/m - 1] 100 = ((1.0718)^1/2 - 1) 100 = (1.0352 - 1) 100 = (0.0352) 100 = 3.52 round one decimal = 3.5 % \r\n R = N ((1 + Re)^1/N - 1) times 100 = 12 ((1 + 0.1741)^1/2 - 1) times 100 = 12 ((1.174)^1/2 - 1) times 100 = 12 (1.0134 - 1) 100 = (12 (0.0134)) 100 = (0.1608) 100 = 16.08 Nominal interest = 1.61 % \r\n Nominal rate = 0 = 5% r = monthly = 12 Re = [1 + 0.05/12]^12 - 1 = [1 + 0.0041]^12 - 1