Question

Given the following information

Month	Bills($)	Income($)
1	0	0
2	50	0
3	50	200
4	50	0
5	50	0
6	50	200
7	50	0
8	50	0
9	50	200
10	50	0
11	50	0
12	50	200

Given a nominal annual interest rate rate of 9.00% compounded monthly,

a) What is the effective quarterly rate?

b) What is the present worth of the bills?

c) what is the present worth of the income?

d) If the effective annual interest rate is 9.38%, and inflation rate is 1.6%, What is the true annual interest rate?

Answer 1

a) Annual interest rate = 9% compounded monthly

Annual Effective Interest rate = [1 + (9% / 12)]^¹² = 1.0938 which is 9.38%

Let quarterly rate of interest be 'r'

1.0938 = [1 + r]^⁴

r = 0.02266 which is 2.266%

b) Present worth of bills is calculated as: [Bills / (1 + Monthly Interest rate)^^Month]

Monthly rate of interest = (9% / 12) = 0.0075

c) Present worth of income is calculated as: [Income / (1 + Monthly Interest rate)^^Month]

Monthly rate of Interest = (9% / 12) = 0.0075

d) Effective annual interest rate = 9.38%

Inflation rate = 1.6%

Annual interest rate = Effective Annual Interest rate - Inflation rate = 9.38% - 1.6% = 7.78%