FI 16 Time Value of Money

Question 1

How are interest rates always shown?

Answer 1

Annually, known as stated or nominal rates

Question 2

What is the EAR?

Answer 2

Effective annual rate. It breaks down the annual rate into an equivalent rate when compounded over more than one period. The more periods, the higher the EAR.

Question 3

Formula for EAR

Answer 3

EAR = (1 + r ÷ n)^n – 1, where r is the quoted rate and n is the number of compounding periods per year
For example, a 6% interest rate compounded quarterly has an EAR calculated as follows:

 EAR = (1 + r ÷ n)^n – 1 = (1 + 0.06 ÷ 4)^4 – 1 = 1.0614 – 1 = 6.14%

Question 4

Formula for Effective Compounding rate

Answer 4

Effective compounding rate = (Effective annual rate + 1)^(1 ÷ n) – 1

where n is the number of compounding periods in a year

For example, if the effective annual rate is 6.17%, what is the effective monthly rate?

 Effective monthly rate = (Effective annual rate + 1)^(1 ÷ n) – 1 = (0.0617 + 1)^ (1 ÷12 ) – 1 = 0.005 = 0.5%

Question 5

Present value of perpetuity with no growth

Answer 5

PV = PMT / i where i = discount rate

Question 6

Present value of perpetuity with constantly growing perpetuity

Answer 6

PV = PMT / i - g where i is the discount rate and g is the growth rate