Question

If you put up $41,000 today in exchange for a 5.1 percent, 15-year annuity, what will the annual cash flow be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

$\large\boxed{\large\boxed{\ 3,976.78}}$

Explanation:

A 15-year annuity is constant cash flow obtained during 15 years. Then, you need to find a current of 15 annual cashflows whose present value is equal to $41,000. That is given by the constant annuity formula.

The formula for a constant annuity is:

         $PV=C\times [\frac{1}{r}-\frac{1}{r(1+r)^t}}]$

Where:

• $PV$ is the present value of the annuity which must be equal to the amount you invest: $41,000

• $r$ is the compounded interest rate: assuming the interest is compounded annually and not monthly it is 5.1% = 0.051

• $t$ is the number of payments: 15 (one by year)

• $C$ is the annual cash flow: what you want to determine.

Substitute in the formula and solve for $C$

         $\ 41,000=C\times [\frac{1}{0.051}-\frac{1}{0.051(1+0.051)^{15}}]$

        $\ 41,000=C\times 10.309853$

        $C=\ 3,976.78$