Question

Loaded-Up Fund charges a 12b-1 fee of 1% and maintains an expense ratio of .75%. Economy Fund charges a front-end load of 2%, but has no 12b-1 fee and an expense ratio of .25%. Assume the rate of return on both funds’ portfolios (before any fees) is 6% per year. How much will an investment in each fund grow to after?
a. 1 year?
b. 3 years?
c. 10 years?

Answer 1

Answer:

a. The amount in Loaded-UP Fund will grow to $104.25 after 1 year, while the amount in the Economy Fund will grow to $103.64 after 1 year.

b. The amount in Loaded-UP Fund will grow to $113.30 after 3 years, while the amount in the Economy Fund will grow to $115.90 after 3 years.

c. The amount in Loaded-UP Fund will grow to $151.62 after 10 years, while the amount in the Economy Fund will grow to $171.41 after 10 years.

Explanation:

The following are the relevant formulae to use:

Amount available in Loaded-UP Fund after a certain year = Investment * (1 + Rate of return – 12b-1 fee – Expense ratio)^Number of years ……………….. (1)

Amount available in Economy Fund after a certain year = Investment * (1 – Front-end load) * (1 + Rate of return – Expense ratio)^Number of years ……………….. (2)

Assuming investment is equal to $100 and using equations (1) and (2), we have:

a. 1 year?

Amount available in Loaded-UP Fund after 3 years = $100 * (1 + 6% - 1% - 0.75%)^1 = $104.25

Amount available in Economy Fund after 3 years = $100 * (1 - 2%) * (1 + 6% - 0.25%)^1 = $103.64

Therefore, the amount in Loaded-UP Fund will grow to $104.25 after 1 year, while the amount in the Economy Fund will grow to $103.64 after 1 year.

b. 3 years?

Amount available in Loaded-UP Fund after 3 years = $100 * (1 + 6% - 1% - 0.75%)^3 = $113.30

Amount available in Economy Fund after 3 years = $100 * (1 - 2%) * (1 + 6% - 0.25%)^3 = $115.90

Therefore, the amount in Loaded-UP Fund will grow to $113.30 after 3 years, while the amount in the Economy Fund will grow to $115.90 after 3 years.

c. 10 years?

Amount available in Loaded-UP Fund after 3 years = $100 * (1 + 6% - 1% - 0.75%)^10 = $151.62

Amount available in Economy Fund after 3 years = $100 * (1 - 2%) * (1 + 6% - 0.25%)^10 = $171.41

Therefore, the amount in Loaded-UP Fund will grow to $151.62 after 10 years, while the amount in the Economy Fund will grow to $171.41 after 10 years.