Question

Suppose you have invested the following sums on the last day of each year in a mutual fund with front-end loads of 4% and management fees of 0.4%. The fund earned 11% per year. How much will you have at the end of year 10?

Year                Cash Flow

    0                       $1600

    1                       $2500

    2                       $3000

Answer 1

Mutual Fund growth rate = 11%

Management fee = 0.4%

Front end load = 4%

Front end load is charged upfront while investing in a mutual fund.

Management fee is charged on yearly basis by deducting the growth rate

Effective growth rate on Mutual Fund = Mutual Fund growth rate - Management fee

Effective growth rate on Mutual Fund = 11% - 0.4%

Effective growth rate on Mutual Fund = 10.6%

For year 0

Cash flow after front end load deduction = Cash flow * (1 - Front end load)

Cash flow after front end load deduction = $1600 * (1 - 4%)

Cash flow after front end load deduction = $1536

Value of cashflow at the end of year 10 = Cash flow after front end load deduction * (1 + Effective growth rate on Mutual Fund)^{10 - year invested}

For year 0

Value of cashflow at the end of year 10 = $1536 * (1 + 10.6%)^{(10 - 0)}

Value of cashflow at the end of year 10 = $4206.71

For year 1

Value of cashflow at the end of year 10 = $2400 * (1 + 10.6%)^{(10 - 1)}

Value of cashflow at the end of year 10 = $5943.02

For year 2

Value of cashflow at the end of year 10 = $2880 * (1 + 10.6%)^{(10 - 2)}

Value of cashflow at the end of year 10 = $6448.13

Year	Cash Flow	Cash flow after front end load deduction	Value of cashflow at the end of year 10
0	$1600	$1536	$4206.71
1	$2500	$2400	$5943.02
2	$3000	$2880	$6448.13

Value of the fund at the end of year 10 = Value of the cash flow at the end of year 10 for year 0 + Value of the cash flow at the end of year 10 for year 1 + Value of the cash flow at the end of year 10 for year 2

Value of the fund at the end of year 10 = $4206.71 + $5943.02 + $6448.13

Value of the fund at the end of year 10 = $16,597.86