### The future value (F) of an annuity

Assignment

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Â Â Â Â Â The future value (F) of an annuity is defined as

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Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â A/F=(1+i)n-1/i

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which means that if you invest A per year at an interest rate if i, you will have F saved up at the end of n years.Â This assumes that you make one investment per year at the end of the year, but the future value does not differ much from the one calculated for monthly or bi-monthly investments, like having investments deducted from a paycheck.

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Your generation will have to invest in what is called defined-contribution plans to save for retirement, because most companies no longer have defined-benefit plans (pension plans).Â The good news is that these contributions can be taken out of your paycheck before taxes, thereby reducing your taxable income, and most companies provide some sort of matching contribution that is not considered part of your income.

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1.Â Â Prepare a plot showing the future value of investing in the stock market, which has a historic rate of return (interest rate) of 8% per year.Â You can always invest as much as you want, but, depending on the investment vehicle and your age, you are permitted to invest between $4000/yr and $15,000/yr while paying no tax on the accumulated interest, and in some cases having the investment deducted from your paycheck before taxes.Â Make the x-axis the number of years of contributions, from 5-40, in increments of 5 years, and the y-axis the future value of the investment.Â There should be lines for investments of $4000/yr, $6,000/yr, $9,000/yr, 12,000/yr, and $15,000/yr.Â This plot should be in an appropriate form, as discussed and illustrated in class.

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2.Â Â Discuss the advantage of starting to invest at age 25 rather than at age 60.

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3.Â Â If you invest $3000/yr for 30 years in conservative fixed-income instruments returning 5% interest,

Â Â Â Â Â Â Â Â Â Â Â a) what is the future value?Â

Â Â Â Â Â Â Â Â Â Â Â b) what is the future value at 8% interest.

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4.Â Â How much would you have to invest per year at 8% interest for 40 years to have a retirement nest egg of $5 million?

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5.Â Â If you invest $5000/yr for 40 years, what rate of return would be required to have a retirement nest egg of $10 million?

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**Posted 06 Jun 2017 08:06 AM**
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