Consider the following four investments. a) You invest $3,000 annually in a mutu
ID: 2726783 • Letter: C
Question
Consider the following four investments.
a) You invest $3,000 annually in a mutual fund that earns 10 percent annually, and you reinvest all distributions. How much will you have in the account at the end of 20 years?
b) 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 reinvest 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.)
c) 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?
d) You invest $3,000 annually in no-load mutual fund that has a 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?
**Please provide work in Excel w/ formulas**
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 fund different?
Explanation / Answer
a Amt Invested 3,000 Duration 20 Years Compounding factor @10% for 20 years =1.1^20= 6.7275 Maturity Value after 20 Years = $ 20,182.50 b Invested Amount 3,000 Less : Load @% 150 Net Amount Invested = 2,850 Compounding factor @10% for 20 years =1.1^20= 6.7275 Maturity Value after 20 Years = $ 19,173.37 c Here the expense ration is 1% after 10% RETURN Maturity Value calculation Beginning value of the year Compounding factor Maturity Value before Expense deduction Deduction of Expense @1% Maturity Value after Expense deduction Year Year 1 3,000 1.10 3,300 33.00 3,267.00 Year 2 3,267 1.10 3,594 35.94 3,557.76 Year 3 3,558 1.10 3,914 39.14 3,874.40 Year 4 3,874 1.10 4,262 42.62 4,219.23 Year 5 4,219 1.10 4,641 46.41 4,594.74 Year 6 4,595 1.10 5,054 50.54 5,003.67 Year 7 5,004 1.10 5,504 55.04 5,449.00 Year 8 5,449 1.10 5,994 59.94 5,933.96 Year 9 5,934 1.10 6,527 65.27 6,462.08 Year 10 6,462 1.10 7,108 71.08 7,037.20 Year 11 7,037 1.10 7,741 77.41 7,663.51 Year 12 7,664 1.10 8,430 84.30 8,345.57 Year 13 8,346 1.10 9,180 91.80 9,088.32 Year 14 9,088 1.10 9,997 99.97 9,897.18 Year 15 9,897 1.10 10,887 108.87 10,778.03 Year 16 10,778 1.10 11,856 118.56 11,737.28 Year 17 11,737 1.10 12,911 129.11 12,781.89 Year 18 12,782 1.10 14,060 140.60 13,919.48 Year 19 13,919 1.10 15,311 153.11 15,158.32 Year 20 15,158 1.10 16,674 166.74 16,507.41 So maturity Value after 20 years = $ 16,507.41 d Amt Invested 3,000 Duration 20 Compounding factor @10% for 20 years =1.1^20= 6.7275 Maturity Value after 20 Years = $ 20,182.50 Less 5% Exit fee= $ 1,009.12 Net Value after 20 years investment : $ 19,173.37 e When $3000 invested every year, The Future value of Annuity = A [(1+k)^n-1]/k where A=3000 per year k=10% pa n=20 years FV=3000*[1.10^20-1]/0.10 FV =$171,825 So the Maturity value will be $171,825 As in this case every year the amount is deposited, the annuity effect for 20 years make the final amount much bigger.
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