Loaded-Up Fund charges a 12b-1 fee of 1% and maintains an expense ratio of 0.70%

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.)

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.)

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.)

Explanation / Answer

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.

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