Question

Find the amount to which $600 will grow under each of these conditions:

1. 6% compounded annually for 3 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $   

2. 6% compounded semiannually for 3 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $   

3. 6% compounded quarterly for 3 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $   

4. 6% compounded monthly for 3 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $   

5. 6% compounded daily for 3 years. Assume 365-days in a year. Do not round intermediate calculations. Round your answer to the nearest cent.

   $   

6. Why does the observed pattern of FVs occur?

Answer 1

a) 6% compounded annually for 3 years.

Future value =600 * (1.06)^3

= $ 714.61

b)6% compounded annually for 3 years.

so rate = 6/2 =3% and time period = 3*2 = 6

  Future value =600 * (1.03)^6

= $ 716.43

c)6% compounded quarterly for 3 years.

so rate = 6/4 =1.5% and time period = 3*4 = 12

  Future value =600 * (1.015)^12

= $ 717.37

d)6% compounded monthly for 3 years.

so rate = 6/12 =0.5% and time period = 3*12 = 36

  Future value =600 * (1.005)^36

= $ 718.01

e)6% compounded daily for 3 years.

so rate = 6/365 =0.016438 % and time period = 3*365 = 1095

  Future value =600 * (1.00016438)^1095

= $ 718.32

f) We can see from the observed pattern , that when the compounding frequency increases for the same time period the future values also increases. That is why the daily compounded Future value is the highest among these.