An investment will pay $100 at the end of each of the next 3 years, $250 at the

Question

An investment will pay $100 at the end of each of the next 3 years, $250 at the end of Year 4, $350 at the end of Year 5, and $500 at the end of Year 6.

If other investments of equal risk earn 10% annually, what is its present value? Round your answer to the nearest cent.

If other investments of equal risk earn 10% annually, what is its future value? Round your answer to the nearest cent

What's the future value of a 12%, 5-year ordinary annuity that pays $300 each year? Round your answer to the nearest cent.

If this was an annuity due, what would its future value be?

You have $22,318.30 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until your account totals $210,000. You expect to earn 11% annually on the account. How many years will it take to reach your goal?

Explanation / Answer

Answer: Calculation of present value:

Calculation of Future value: Technically, as we assumed no salvage value then the future value will be zero if you are asking how much remains in the investment. If you are asking how much the investment has yielded, keep in mind that the cash flows are not by definition reinvested so the time value of those cash flows can't be accounted for. If you do not account for the time value of those cash flows then the future value is just:

$100 * 3 + $250 + $350 + $500 = $1,400

However if you use the 10% per annum effective rate as a discount rate to take into consideration the time value of the money which is basically saying that you can reinvest the cash flows at 10% per annum effective then the future value would be:

$100 * 1.10^5 + $100 * 1.10^4 + $100 * 1.10^3 + $250 * 1.10^2 + $350 * 1.10 + 500 = $1628.061

Answer: Calculation of Future value of a 12%, 5-yer ordinary annuity: The future value. FV, of an ordinary annuity with interest compounded at the end of each payment interval, is given by:

FV = B{(1+i)n - 1}/i

=$300{(1+0.12)5 - 1}/0.12

=228.70250496/0.12

=$1905.85

Answer: PV =$22318.30

PMT = $3000

FV = $210000

I =11%

n = 12years

Cash Flow time PVF (10%) PV ($) 100 1 0.909 90.9 100 2 0.826 82.6 100 3 0.751 75.1 250 4 0.683 170.75 350 5 0.621 217.35 500 6 0.564 282 Total 918.7

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