Question

Loaded-Up Fund charges a 12b-1 fee of 1% and maintains an expense ratio of 0.70%. Economy Fund charges a front-end load of 2%, but has no 12b-1 fee and an expense ratio of 0.30%. Assume the rate of return on both funds’ portfolios (before any fees) is 7% per year.

a. How much will an investment of $100 in each fund grow to after 1 year? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Loaded-Up Fund	$
Economy Fund	$

b. How much will an investment of $100 in each fund grow to after 4 years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Loaded-Up Fund	$
Economy Fund	$

c. How much will an investment of $100 in each fund grow to after 13 years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Loaded-Up Fund	$
Economy Fund	$

Answer 1

Solution:
a.	Loaded-Up Fund	$105.30
	Economy Fund	$104.57
Working Notes:
	Loaded-Up Fund
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	True expense ratio = Expense ratio + 12b-1 fee
	True expense ratio for loaded fund = Expense ratio + 12b-1 fee
		= 0.70 % + 1%
		=1.70 %
	Investment = $100
	Front end load = 0%
	rate of return = 7%
	True expense ratio = 1.70%
	T = 1 years
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	=$100 x (1-0%) x (1+7% - 1.70%)^1
	=$100 x 1 x (1+0.07-0.017)^1
	=$105.30
	Economy Fund
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	True expense ratio = Expense ratio + 12b-1 fee
	True expense ratio for loaded fund = Expense ratio + 12b-1 fee
		= 0.30 % +0%
		=0.30 %
	Investment = $100
	Front end load = 2%
	rate of return = 7%
	True expense ratio = 0.30%
	T = 1 years
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	=$100 x (1-2%) x (1+7% - 0.30%)^1
	=$100 x 0.98 x (1+0.07-0.003)^1
	=$104.566
	=$104.57
b.	Loaded-Up Fund	$122.95
	Economy Fund	$127.02
Working Notes:
	Loaded-Up Fund
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	True expense ratio = Expense ratio + 12b-1 fee
	True expense ratio for loaded fund = Expense ratio + 12b-1 fee
		= 0.70 % + 1%
		=1.70 %
	Investment = $100
	Front end load = 0%
	rate of return = 7%
	True expense ratio = 1.70%
	T = 4 years
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	=$100 x (1-0%) x (1+7% - 1.70%)^4
	=$100 x 1 x (1+0.07-0.017)^4
	=$100 x (1.053)^4
	=$122.9457398
	=$122.95
	Economy Fund
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	True expense ratio = Expense ratio + 12b-1 fee
	True expense ratio for loaded fund = Expense ratio + 12b-1 fee
		= 0.30 % +0%
		=0.30 %
	Investment = $100
	Front end load = 2%
	rate of return = 7%
	True expense ratio = 0.30%
	T = 4 years
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	=$100 x (1-2%) x (1+7% - 0.30%)^4
	=$100 x 0.98 x (1+0.07-0.003)^4
	=$100 x 0.98 x (1.067)^4
	=$127.02341
	=$127.02
c.	Loaded-Up Fund	$195.69
	Economy Fund	$227.70
Working Notes:
	Loaded-Up Fund
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	True expense ratio = Expense ratio + 12b-1 fee
	True expense ratio for loaded fund = Expense ratio + 12b-1 fee
		= 0.70 % + 1%
		=1.70 %
	Investment = $100
	Front end load = 0%
	rate of return = 7%
	True expense ratio = 1.70%
	T = 13 years
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	=$100 x (1-0%) x (1+7% - 1.70%)^13
	=$100 x 1 x (1+0.07-0.017)^13
	=$100 x (1.053)^13
	=$195.69009
	=$195.69
	Economy Fund
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	True expense ratio = Expense ratio + 12b-1 fee
	True expense ratio for loaded fund = Expense ratio + 12b-1 fee
		= 0.30 % +0%
		=0.30 %
	Investment = $100
	Front end load = 2%
	rate of return = 7%
	True expense ratio = 0.30%
	T = 13 years
	Value of investment at end of Tth year = Investment amount (1-Fornt end load ) x ( 1+ rate of return - true expense ratio)^T
	=$100 x (1-2%) x (1+7% - 0.30%)^13
	=$100 x 0.98 x (1+0.07-0.003)^13
	=$100 x 0.98 x (1.067)^13
	=$227.700261
	=$227.70
Please feel free to ask if anything about above solution in comment section of the question.