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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.)

Respuesta :

Edufirst

Answer:

[tex]\large\boxed{\large\boxed{\$ 3,976.78}}[/tex]

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:

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

Where:

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

  • [tex]r[/tex] is the compounded interest rate: assuming the interest is compounded annually and not monthly it is 5.1% = 0.051

  • [tex]t[/tex] is the number of payments: 15 (one by year)

  • [tex]C[/tex] is the annual cash flow: what you want to determine.

Substitute in the formula and solve for [tex]C[/tex]

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

        [tex]\$ 41,000=C\times 10.309853[/tex]

        [tex]C=\$ 3,976.78[/tex]

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