Question

Loaded-Up Fund charges a 12b-1 fee of 1% and maintains an expense ratio of 0.85% Economy Fund charges a front-end load of 2%, but has no 12b-1 fee and an expense ratio of 0.15% Assume the rate of return on both funds portfolios (before any fees) is 10% per year.
How much will an investment of $100 in each fond grow to after 1 year?

How much will an investment of $100 in each fond grow to after 8 years?

When will an investment of $100 in each fund grow to the same amount?

Answer 1

ANSWER:

1) Loaded-Up Fund = $ 108.15

Economy Fund = $ 107.65

2) Loaded-Up Fund = $187.16

Economy Fund = $207.79

3) 1.2953years = 15.54months, approximately 16months

EXPLANATION:

Labelling of values;

Loaded-Up Fund 12b-1 fee (b1) = 1%

Loaded-Up Fund front end load (f1) = 0%

Loaded-Up Fund expense ratio (e1) = 0.85%

Economy Fund 12b-1 fee (b2) = 0%

Economy Fund front end load (f2) = 2%

Economy Fund expense ratio (e2) = 0.15%

Loaded-Up Fund returns is also the Economy Fund returns = r1 = r2 = 10%

Therefore;

Returns from a fund = (1 - f) × (1 + (r - b - e))^n............(1)

Where;

Investment final value = Investment amount × (1 + return from the fund)

Therefore, equation becomes:

Investment amount × (1 - f) × (1 + (r - b - e))^n............(2)

(1)

Using equation 2

Investment amount = $100

Number of years = n = 1

Substitute the given values for

LOADED-UP FUND:

Investment final value = $100 × (1 - 0%) ×(1 + (10% - 0.1% - 0.85%))^1

= $108.15

ECONOMY FUND:

Investment final value = $100 × (1 - 2%) × (1 + (10% - 0% - 0.15%))^1

= $107.65

Therefore the investment of $100 in one year will become;

Loaded-Up Fund = $ 108.15

Economy Fund = $ 107.65

(2)

Using equation 2

Investment amount = $100

Number of years (n) = 8

Substitute the given values for

LOADED-UP FUND:

Investment final value = $100 × (1 - 0%) ×(1 + (10% - 0.1% - 0.85%))^8

= $187.16

ECONOMY FUND:

Investment final value = $100 × (1 - 2%) × (1 + (10% - 0% - 0.15%))^8

= $207.79

Therefore the investment of $100 in 8 years will become;

Loaded-Up Fund = $187.16

Economy Fund = $207.79

(3)

To find n, we equate loaded-up fund with economy fund.

Therefore;

$100 × (1 - 0%) ×(1 + (10% - 0.1% - 0.85%))^n = 100 × (1 - 2%) × (1 + (10% - 0% - 0.15%))^n

Solving out gives;

100 × (1.0815)^n = 98 × (1.0985)^n

Cross multiplying gives;

100/98 = (1.0985/1.0815)^n

Taking the natural log of both side;

n × ln(1.0985/1.0815) = ln(100/98)

Therefore

n(0.015597) = 0.020203

n = 0.020203 ÷ 0.015597 = 1.295324

n = 1.3 years

To check n in months, 1.295324 × 12 = 15.59 which will be approximately 16months