Question

Suppose that weekly interest rate is 0.1% in this year. In the next year, weekly interest rate becomes 0.2%. Assume that there are 52 weeks in a year.

a. What are the Annual Percentage Rates (APR) in the first and second years?

b. What are the Effective Annual Rates (EAR) in the first and second years?

c. What is the future value of $1 after 2 years?

d. What is the present value of a payment of $1 to be received in 2 years?

e. What would be the change of purchasing power of today’s $1 in 2 years if there is an annual inflation rate of 3%?

Answer 1

(a) First year

Weakly rate = 0.1% /week

Annual percentage rate = 52 weeks/year * 0.1% /week = 5.2% per year

Second year

Weakly rate = 0.2% /week

Annual percentage rate = 52 weeks/year * 0.2% /week = 10.4% per year

(b)

First year:

Weakly rate = 0.1% /week

Let R1 be the Effective annual rate (EAR)

[1 + R1]^1 = [1 + 0.1%]^52

[1 + R1] = 1.05334

R1 = 0.05334 = 5.334%

Second year:

Weakly rate = 0.2% /week

Let R2 be the Effective annual rate (EAR)

[1 + R2]^1 = [1 + 0.2%]^52

[1 + R2] = 1.10948

R2 = 0.10948 = 10.948%

(C) Future value of $1 after 2 years

$1 * [1 + R1] * [1 + R2]

$1 * [1+5.334%]*[1+10.948%] = $1.168665 (amount)

(d) Present value of $1 to be received in 2years

PV = $1/[1+5.334%]*[1+10.948%] = $0.856