Rate of Interest

Rate by which Principal amount increase with the time period. There are three types of interest

1-      Nominal rate of interest

2-      Effective rate of interest

3-      Equivalent rate of interest

1)      Nominal rate of interest:

When rate of interest is apply for one year or the rate which is written on the document is called nominal rate of interest.

2)      Effective rate of interest:

When nominal rate of interest is apply on quarterly basis or monthly basis is called effective rate of interest. Because effectiveness of interest increase due to shorter period compounding.

Effective rate of interest = [1+r/m]^n*m100

m = no. of compounding periods

r = nominal rate of interest

3)      Equivalent rate of interest:

Whenever two different rate of interest for different time periods give the same future value is called equal lent rate of interest

For example 18 % per annum = 1.38888843 % per month will give us the same future value

Equal lent rate of interest = [(1+r_y)^1/m-1]100

m  = no. of periods

Q no 10:

Suppose you were to receive $ 1000 at the end of 10 year. If your opportunity rate is 10 percent, what is the present value of this if interest is compounded a) annually? (b)quarterly?(c)continuously ?

Solution:

When annually interest rate:

F.V = $ 1000

n = 10 year

r = 10 %

P.V =F.V (1+r)^-n

P.V = 1000(1+0.10)^-10

P.V = $ 385.55

When interest rate is quarterly:

P.V = F.V (1+r/m)^-n*m

P.V = 1000(1+0.10/4)^-10*4

P.V = $ 372.43

When interest rate continuously:

P.V = F. V (e)^-r*n

Where

e = 2.71828

P.V = $ 367.89