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# Future value of an ordinary annuity

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1.James plans to fund his individual retirement account, beginning today, with 20 annual deposits of \$2,000, which he will continue for the next 20 years. If he can earn an annual compound rate of 8 percent on his deposits, the amount in the account upon retirement will be

1. 1. \$21,207.
2. 2. \$91,524.
3. 3. \$98,846.
4. 4. \$19,636.

2.A generous benefactor to the local ballet plans to make a one-time endowment which would provide the ballet with \$150,000 per year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment be?

1. 1. \$ 750,000
2. 2. \$3,000,000
3. 3. \$ 300,000
4. 4. \$1,428,571

3.The future value of a \$10,000 annuity due deposited at 12 percent compounded annually for each of the next 5 years is

1. 1. \$63,530.
2. 2. \$40,376.
3. 3. \$36,050.
4. 4. \$71,154.

4.The future value of an ordinary annuity of \$2,000 each year for 10 years, deposited at 12 percent, is

1. 1. \$11,300.
2. 2. \$35,098.
3. 3. \$39,310.
4. 4. \$20,000.

5.Indicate which of the following is true about annuities.

1. 1. An ordinary annuity is an equal payment paid or received at the beginning of each period.
2. 2. An ordinary annuity is an equal payment paid or received at the end of each period that increases by an equal amount each period.
3. 3. An annuity due is a payment paid or received at the beginning of each period that increases by an equal amount each period.
4. 4. An annuity due is an equal payment paid or received at the beginning of each period.

#### Solution Preview

1.James plans to fund his individual retirement account, beginning today, with 20 annual deposits of \$2,000, which he will continue for the next 20 years. If he can earn an annual compound rate of 8 percent on his deposits, the amount in the account upon retirement will be

1. 1. \$21,207.
2. 2. \$91,524.
3. 3. \$98,846.
4. 4. \$19,636.
Here we have to find out the compounded value of annuity
F=A*((1+r)^n-1)/r*(1+r)
F=Future value, A= Annuity r= rate of interest n=duration

Through Above formulae Through excel
A= 2000, r= 8%, n=20 91523.93 \$91,523.93