Suppose a 100000 investment grows 3 during the first year an

Suppose a $100,000 investment grows 3% during the first year and 4% during the second year. By what percent will it have grown after the two-year period? Rework Exercise 1 for the case where the investment earns 4% during the first year and 3% during the second year. Is the answer to Exercise 2 greater than, less than, or equal to the answer to Exercise 1? Consider an annuity in which $100,000 is invested and $10,000 is withdrawn at the end of each year. Suppose the interest rate is 3% during the first year and 4% during the second year. What is the balance at the end of the second year? Rework Exercise 3 where the interest rate is 4% during the first year and 3% during the second year. Is the balance at the end of the second year greater than, less than, or equal to the answer to Exercise 3? Explain why your answer to this question makes sense.

Solution

1.

Let investment be I=100000 dollars

Amount at end of first year ,A1= (1+3/100)I=1.03I

Amount at the end of second year, A2=(1+4/100)A1=1.04A1=1.04*1.03I=1.0712I

Hence total percent growth is: 100(1.072I-I)/I=7.12%

2.

Let investment be I=100000 dollars

Amount at end of first year ,A1= (1+4/100)I=1.04I

Amount at the end of second year, A2=(1+3/100)A1=1.03A1=1.03*1.04I=1.0712I

Hence total percent growth is: 100(1.072I-I)/I=7.12%

Answer is equal to that in Exercise I

3.

Initial investment, A=100000

Amount at the end of first year after including the end of year withdrawal and interest is:

A1=(1+3/100)A-10000=1.03*100000-10000=103000-10000=93000 dollars

Amount at the end of second year is:

A2=(1+4/100)A1-10000=1.04*93000-10000=86720 dollars

4.

Initial investment, A=100000

Amount at the end of first year after including the end of year withdrawal and interest is:

A1=(1+4/100)A-10000=1.04*100000-10000=104000-10000=94000 dollars

Amount at the end of second year is:

A2=(1+3/100)A1-10000=1.03*94000-10000=86820 dollars

The balance is greater than the balance in Exercise 3.

This is expected because in Exercise 3 4% interest is on balance after first year but in Exercise 4 4% interest is on initial investement and 3% on the balance after first year.