Question

5. Compare two scenarios: scenario A has interest rate of 6%, scenario B has interest rate of 6% minus 80 basis points (so net 5.2%) paid in fees. How much longer did it take to double your investment?

6. As before, scenario A has interest rate of 6%, scenario B has interest rate of 6% minus 80 basis points (so net 5.2%) paid in fees. After 10 years, how much less is a portfolio that started with $1000 worth under scenario B?

Answer 1

Question 5:

Scenario A

r = 6%

$2 = $1 *(1+6%)^n

(1.06)^n = 2

n = 11.8957 years

Scenario B

r = 5.2%

$2 = $1 *(1+5.2%)^n

(1.052)^n = 2

n = 13.6734 years

Additional years to double the investment = Number of years under Scenario B - Number of years under Scenario B

=13.6734 - 11.8957

= 1.7777 years

Therefore, it will take additional 1.78 years to double the investment

Question 6:

Scenario A

r = 6%

Present Value = $1,000

n = 10 years

Amount at the end of 10 years = $1,000 * (1+6%)^10

= $1,000 * 1.7908477

= $1,790.8477

Amount at the end of 10 years is $1,790.85

Scenario B

r = 5.2%

Present Value = $1,000

n = 10 years

Amount at the end of 10 years = $1,000 * (1+5.2%)^10

= $1,000 * 1.66018849

= $1,660.18849

Amount at the end of 10 years is $1,660.19

Additional amount = Amount in the Scenatio A - Amount in the Scenario B

=  $1,790.85 - $1,660.19

= $130.66

Therefore, The amount by wich scenario B is less than Scenario A is $130.66