Question

7. How much will Adrian have if he allows his investment to remain in the mutual fund for 10 years?

8. How much will Clemens have if he allows his investment to remain in the index fund for 10 years?

9. How much more value does Clemens's investment generate than Adrian's in 10 years' time?

10. What about over 40 years' time

Answer 1

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Suppose both Adrian and Clemens invest $10,000 in a mutual fund.

Lets think of it another way so that we can see the impact of compounding on this investment. For simplicity's sake, we will assume that Adrian's rate of return is effectively 5.7% annually (7% - 1.3% fee) and Clemens's rate of return is effectively 6.8% annually (7% - 0.2% fee).

7. How much will Adrian have if he allows his investment to remain in the mutual fund for 10 years?

8. How much will Clemens have if he allows his investment to remain in the index fund for 10 years?

9. How much more value does Clemens's investment generate than Adrian's in 10 years' time?

10. What about over 40 years time?

Answer:

7. Adrian's amount = $17,408

8. Clemens's amount = $19,306

9. Difference in amount after 10 years = $1,898

10. Difference in amount after 40 years = $47,114

Step-by-step explanation:

7. How much will Adrian have if he allows his investment to remain in the mutual fund for 10 years?

Adrian will have a amount given by

`A = P*(1+r)^(n)`

Where P is the invested amount, r is the annual rate of return and n is the number of years.

Here P = 10,000, r = 0.057, n = 10

`A = 10,000*(1+0.057)^(10)\\\\A = 10,000* 1.7408\\\\A = \$17,408`

8. How much will Clemens have if he allows his investment to remain in the index fund for 10 years?

Clemens will have a amount given by

`A = P*(1+r)^(n)`

Here P = 10,000, r = 0.068, n = 10

`A = 10,000*(1+0.068)^(10)\\\\A = 10,000* 1.9306\\\\A = \$19,306`

9. How much more value does Clemens's investment generate than Adrian's in 10 years' time?

`\text {Difference} = \$19,306 - \$17,408 = \$1,898`

Therefore, Clemens's investment generate $1,898 more as compared to Adrian's in 10 years time period.

10. What about over 40 years time ?

Adrian's amount:

Here P = 10,000, r = 0.057, n = 40

`A = 10,000*(1+0.057)^(40)\\\\A = 10,000* 9.1833\\\\A = \$91,833`

Clemens's amount:

Here P = 10,000, r = 0.068, n = 40

`A = 10,000*(1+0.068)^(40)\\\\A = 10,000* 13.8947\\\\A = \$138,947`

`\text {Difference} = \$138,947 - \$91,833 = \$47,114`

Therefore, Clemens's investment generate $47,114 more as compared to Adrian's in 40 years time period.