Time Line

I (1) The future value will be larger if we compound an initial amount more often than annually, for example, every 6 months, or semiannually, holding the stated interest rate constant.

If we invested our money for five years at 8 percent interest compounded semiannually, we are really investing our money for 10-six month’s period during which we receive 4 percent interest each period. And for that reason the future value will be larger for semiannually than annually compound.

For example,

Investment=$100

i=15%

n=4

For annual basis your future value will be,

FVn=pv( 1+ i)n

FV= 100 (1+.15)4

= 174.90

FVn=pv( 1+ i/m )mn

=100(1+.15/2)2*4

= 178.35

Whereas,

FVn= the future value of the investment at the end of n years.

n = the number of years during which the compounding occurs.

i= annual interest rate

PV= the present value or original amount invested at the beginning of the first year.

m= the number of times compounding occurs during the year.

I(2)Nominal rate:

The percentage of annual interest which would be earned from a fixed income investment (for example, bonds) if the security was purchased at par value; actual rate of return is usually different. A rate of interest as quoted, rather than the effective rate to which it is equivalent.

The periodic rate:

The interest rate described in relation to a specific amount of time. For example, the monthly periodic rate is the cost of credit per month; the daily periodic rate is the cost of credit per day.

Effective annual rate (EAR):

This is the rate that produce same ending(or future) value under annual compounding as would more frequent compounding at a given nominal rate.

3. Compounded for semiannually

Effective annual rate= EAR= ( 1+ inom/m)m – 1.0

= ( 1+ .10/2)2 – 1.0

=10.25%

Here, inom=10%, m= 2

Compounded for quarterly

Effective annual rate= EAR= ( 1+ inom/m)m – 1.0...