Question

You are offered an annuity that will pay $23,000 per year for 9 years (the first payment will be made today). If you feel that the appropriate discount rate is 10%, what is the annuity worth to you today?

$312,327.97

$145,703.30

$132,457.55

$343,560.77

$259,008.08

Answer 1

ANSWER = $132,457.55

P = $23,000

r = 10% = 0.1

n = 9yrs

$\fn_cm PV\, of\, Annuity = P\left [ \frac{1 - \frac{1}{(1 + r)^{n}}}{r} \right ]$

$\fn_cm PV\, of\, Annuity = P\left [ \frac{1 - \frac{1}{(1 + 0.1)^{9}}}{0.1} \right ]$

$\fn_cm PV\, of\, Annuity = P\left [ \frac{1 - \frac{1}{(1.1)^{9}}}{0.1} \right ]$

$\fn_cm PV\, of\, Annuity = P\left [ \frac{1 - \frac{1}{(2.357947691)}}{0.1} \right ]$

$\fn_cm PV\, of\, Annuity = P\left [ \frac{1 - 0.42409761837}{0.1} \right ]$

$\fn_cm PV\, of\, Annuity = P\left [ \frac{0.57590238163}{0.1} \right ]$

$\fn_cm PV\, of\, Annuity = 23,000 \times 5.7590238163$

$\fn_cm PV\, of\, Annuity = 132,457.55$