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our uncle is about to retire, and he wants to buy an annuity that will provide him with $57,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today?

Respuesta :

TomShelby

Answer:

It cost him 640,617 dollars

Explanation:

as the first payment start today we will calculate the present value for an annuity-due of 57,000 for 20 years discounted at 5.25%

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

C 52,500

time 20

rate 0.0525

[tex]52500 \times \frac{1-(1+0.0525)^{-20} }{0.0525} = PV\\[/tex]

PV $640,617