Question

1. $100,000 is invested for 20 years at 5%. What are the proceeds using:

1. simple interest
2. annual compound interest
3. semi-annual compounding?

2. In the question above, what must the annual compounding rate be in order to produce the same proceeds as 5% semi-annual? What must the quarterly compounding rate be in order to produce the same proceeds as 5% semi-annual?

Answer 1

a) Using Simple interest

Total Amt= Principal +Principal * rate%* time

=100000+100000*5%*20

=200000 $

b) Compound interest

=100000 (1+r%)  20 where r=5%

=100000*2.653

=265300 $

c) Semi annual compounding

=100000(1+.025)40

Where r=5/2=2.5%

=100000*2.69 (rounding off to nearest two decimal nos.)

=269000 $

Calculation of annual compounding rate in order to produce the same proceeds as 5% semi-annual

Let the required rate be r, therefore, according to the question

Proceeds of semi annual rate =100000(1+r)2

269000=100000(1+r)20

2.69=(1+r)20 10^ (log2.69)/20)-1)

Solving for r, 10^ (log2.69)/20)-1) using Log table, r= 5.07%

Calculation of quarterly compounding rate in order to produce the same proceeds as 5% semi-annual

Proceeds of semi annual rate =100000(1+0.25r)n*4 where n stands for period

269000= (1+0.25r)80 Solving for r, 10^ (log2.69)/40)-1) using Log table, r= 2.5% quarterly r =10.02% p.a