Question

You are considering an investment in a mutual fund with a 5% load and expense ratio of 0.1%. You can invest instead in a bank CD paying 2% interest a. If you plan to invest for 2 years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? Assume annual compounding of returns. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual rate of return % b. What annual rate of return must the fund portfolio earn if you plan to invest for 9 years to be better off in the fund than in the CD? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual rate of return % c. Now suppose that instead of a front-end load the fund assesses a 12b-1fee of 80% per year. What annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual rate of return %

Answer 1

Answers:

a. 4.75%

b. 2.49%

c. 3.05%

Step by Step Explanation:

Part 1:

.

The value of CD after 2 years will be:

= PV * ( 1 + rate)ⁿ

= PV * ( 1 + 2%)²

= PV * (1.02)²

The value of mutual fund after 2 years:

Assume that return on mutual funds is x%

Then,

=PV * (1- load) * (1 + rate - expense ratio)²

= PV* (1-0.05) * (1 + x - 0.001)²

= PV * 0.95* (0.999 + x)²

.

If value of mutual fund and value of CD are equal after 2 years then rate will be:

PV * (1.02)² = PV * 0.95* (0.999 + x)²

PV * (1.02)² = 0.95 PV * ( x + 0.999)²

(1.02)² = 0.95 * ( x + 0.999)²

(1.02)² / 0.95 = ( x + 0.999)²

1.0404/ 0.95 = ( x + 0.999)²

1.095157894 = ( x + 0.999)²

(1.095157894)^1/2 = x + 0.999

X = 1.0464979187 - 0.999

X = 0.04749791877 or 4.75%

.

Part B:

The value of CD after 9 years will be:

= PV * ( 1 + rate)ⁿ

= PV * ( 1 + 2%)9

= PV * (1.02)9

The value of mutual fund after 9 years:

Assume that return on mutual funds is x%

Then,

=PV * (1- load) * (1 + rate - expense ratio)²

= PV* (1-0.05) * (1 + x - 0.001)9

= PV * 0.95* (0.999 + x)9

If value of mutual fund and value of CD are equal after 2 years then rate will be:

PV * (1.02)9 = PV * 0.95* (0.993 + x)⁶

PV * (1.02)9 = 0.95 PV * ( x + 0.993)⁶

(1.02)⁹ = 0.95 * ( x + 0.999)9

(1.02)⁹ / 0.95 = ( x + 0.999)9

(1.02)⁹ / 0.95 = (x + 0.999)9

1.195092568 = (x + 0.999)9

( 1.195092568)^1/9 = x + 0.999

1.0239482341185 = x + 0.999

X = 1.0239482341185 - 0.999

X = 0.0249482 or 2.49 %

.

Part C:

The value of CD after 1 years will be:

= PV * ( 1 + rate)ⁿ

= PV * ( 1 + 2%)

= PV * (1.02)

The value of mutual fund after 9 years:

Assume that return on mutual funds is x%

Then,

=PV * (1 + rate - expense ratio)

= PV* (1 + x - 0.001-0.0095)

= PV * ( X + 0.9895)

If value of mutual fund and value of CD are equal after 2 years then rate will be:

PV * (1.02) = PV * (X + 0.9895)

(1.02) = (X + 0.9895)

X = 1.02 - 0.9895

X = 0.0305

X = 3.05%