Question

Mark Ventura has just purchased an annuity to begin payment two years from today. The annuity is for $8,000 per year and is designed to last 10 years. If the interest rate for this problem calculation is 13 percent, what is the most he should have paid for the annuity?

Answer 1

Answer:

• $38,415.88

Explanation:

1. Calculate the value of the annuity one year from now.

The following equation is used to calculate the present value of an annuity that starts payments one year from now:

      $PV=C\times \bigg[\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}\bigg]$

Where:

• PV is the present value
• C is the constant annuity: $8,000
• r is the interest rate: 13% = 0.13
• t is the number of years: 10

Substitute and compute:

        $PV=\ 8,000\times \bigg[\dfrac{1}{0.13}-\dfrac{1}{0.13(1+0.13)^{10}}\bigg]$

        $PV=\ 43,409.95$

Notice that, since the annuity will begin the payment two years from today, that value is the value in a year. Then, to find the value today you must discount the calculated value one year, at the same rate.

2. Value today

      $V_{today}=\dfrac{PV}{(1+r)}=\dfrac{\ 43,409.95}{1.13}=\ 38,415.88$