Your invest $3,000 annually in a mutual fund that earns 10 percent annually and you invest all distributors. How much will you have in the account at the end of 20 years?
You invest $3,000 annually in a mutual fund with a 5 percent load fee so that only $2,850 is actually invested in the fund. The fund earns 10 percent annually, and you invest all distributions. How much will you have in the account at the end of 20 years? Assume that all distributions are not subject to the load fee.
You invest $3,000 annually in a no load mutual fund that charges 12b-1 fees of 1 percent. The fund earns 10 percent annually before fees, and you reinvest all distributions. How much will you have in the account at the end of 20 years?
You invest $3,000 annually in no-load mutual fund that has 5 percent exit fee. The fund earns 10 percent annually before fees, and you reinvest all distributions. How much will you have in the account at the end of 20 years?
In each case you invest the same amount ($3,000) every year, the fund earns the same return each year (10 percent), and you make each investment for the same time period (20 years). At the end of the 20 years, you withdraw the funds. Why is the final amount in each mutual funds different?
To calculate the final amount in each mutual fund, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Let's calculate the final amount for each scenario:
1. Investing $3,000 annually in a mutual fund that earns 10 percent annually and reinvest all distributions:
In this case, the principal amount is $3,000, the annual interest rate is 10% (or 0.1 as a decimal), interest is compounded once per year (n = 1), and the investment is made for 20 years (t = 20).
Using the compound interest formula:
A = 3000(1 + 0.1/1)^(1*20)
A = 3000(1 + 0.1)^20
A ≈ $ 124,098.11
Therefore, you would have approximately $124,098.11 in the account at the end of 20 years.
2. Investing $3,000 annually in a mutual fund with a 5 percent load fee so that only $2,850 is actually invested in the fund:
In this case, the principal amount is $2,850 (since $150 is deducted as the load fee), the annual interest rate is 10%, interest is compounded once per year (n = 1), and the investment is made for 20 years (t = 20).
Using the compound interest formula:
A = 2850(1 + 0.1/1)^(1*20)
A = 2850(1 + 0.1)^20
A ≈ $ 118,893.97
Therefore, you would have approximately $118,893.97 in the account at the end of 20 years.
3. Investing $3,000 annually in a no-load mutual fund that charges 12b-1 fees of 1 percent:
In this case, the principal amount is $3,000, the annual interest rate is 10%, interest is compounded once per year (n = 1), and the investment is made for 20 years (t = 20).
However, since there is a 12b-1 fee of 1%, we need to account for that in the calculations. Each year, 1% of the principal amount ($3,000) will be deducted as fees before calculating the interest.
Using the compound interest formula:
A = (3000 - (3000*0.01))(1 + 0.1/1)^(1*20)
A = 2970(1 + 0.1)^20
A ≈ $ 123,020.20
Therefore, you would have approximately $123,020.20 in the account at the end of 20 years.
4. Investing $3,000 annually in a no-load mutual fund that has a 5 percent exit fee:
In this case, the principal amount is $3,000, the annual interest rate is 10%, interest is compounded once per year (n = 1), and the investment is made for 20 years (t = 20).
However, since there is a 5% exit fee, when withdrawing the funds at the end of 20 years, 5% of the final amount will be deducted as fees.
Using the compound interest formula:
A = 3000(1 + 0.1/1)^(1*20)
A = 3000(1 + 0.1)^20
A ≈ $ 124,098.11
At the end of 20 years, if you withdraw the funds, a 5% exit fee will be applied to the final amount:
Exit fee = 0.05 * $ 124,098.11
Exit fee ≈ $ 6,204.91
Final amount after deducting the exit fee:
A - Exit fee ≈ $ 117,893.20
Therefore, you would have approximately $117,893.20 in the account at the end of 20 years.
The final amount in each mutual fund is different due to the fees and expenses associated with each fund. Load fees, 12b-1 fees, and exit fees reduce the amount of money invested or withdrawn, resulting in a lower final amount compared to the no-load fund without any fees.