question 23 1.5 points a financial contract that pays $2,000 at the beginning of each year for 50 years is…

question 23 1.5 points a financial contract that pays $2,000 at the beginning of each year for 50 years is called a(n) ____ and has a value today of $____ at a required return of 12%. (round to the nearest dollar) a annuity due; $18,602 b annuity due; $16,609 c annuity in arrears; $16,609 d ordinary annuity; $16,609 e perpetuity; $18,602

question 23 1.5 points a financial contract that pays $2,000 at the beginning of each year for 50 years is called a(n) ____ and has a value today of $____ at a required return of 12%. (round to the nearest dollar) a annuity due; $18,602 b annuity due; $16,609 c annuity in arrears; $16,609 d ordinary annuity; $16,609 e perpetuity; $18,602

Answer

Explanation:

Step1: Identify the annuity type

Since payment is at the beginning of each year, it is an annuity - due.

Step2: Use the annuity - due present - value formula

The formula for the present value of an annuity - due is $PV = A\times\frac{1-(1 + r)^{-n}}{r}\times(1 + r)$, where $A=$2000$, $r = 0.12$, and $n = 50$. First, calculate $(1 + r)^{-n}=(1 + 0.12)^{-50}$. $(1 + 0.12)^{-50}=\frac{1}{(1 + 0.12)^{50}}\approx0.00346$. Then, calculate $\frac{1-(1 + r)^{-n}}{r}=\frac{1 - 0.00346}{0.12}=\frac{0.99654}{0.12}\approx8.3045$. Finally, $PV=2000\times8.3045\times(1 + 0.12)=2000\times8.3045\times1.12=$18602$.

Answer:

A. Annuity due; $18,602