Copyright

What is the present value of the following annuity $4,659 every half year at the beginning of the...

Question:

What is the present value of the following annuity $4,659 every half year at the beginning of the period for the next 5 years, discounted back to the present at 13.86% per year, compounded semiannually? Round the answer to two decimal places.

Annuity Value:

The present value of the annuity is the discounted present sum of the equal payments received over time. When the first payment is received right away, it is an annuity due.

Answer and Explanation:


The present value of the annuity due is $35,104.06


The formula for annuity due is:

{eq}PV= C + ( C\times \dfrac{1-(1+r)^{-(n-1)}}{r} ) {/eq}

Here:

Present value (PV) is required

Payment (C) = $4659

r (rate) =13.86% / 2 = 6.93% or 0.0693

n = 5 * 2 = 10

Substituting the formula:

{eq}PV = $4659 + ($4659 \times \dfrac{1-(1+0.0693)^{-(10-1)}}{0.0693}) {/eq}

{eq}PV = $4659 + ($4659 \times 6.534677574) {/eq}

{eq}PV = $4659 + $30,445.06 {/eq}

{eq}PV = $35,104.06 {/eq}


Explore our homework questions and answers library