Question

You are saving for a Porsche Carrera Cabriolet, which currently sells for nearly half a million dollars. Your plan is to deposit $30,800 at the end of each year for the next 11 years. You expect to earn 7 percent each year. Required: 1. Determine how much you will have saved after 11 years. 2. Determine the amount saved if you were able to deposit $33,300 each year. 3. Determine the amount saved if you deposit $30,800 each year, but with 11 percent interest.

Answer 1

Answer:

• 1. $486,134.86

• 2. $525,593.86

• 3. $602,492.04

Explanation:

You need to use the formula to calculate the future value of a constant annual deposit:

      $Future\text{ }value=Deposit\times \bigg[\dfrac{(1+r)^n-1}{r}\bigg]$

Where r is the expected percent return, and n the number of years.

1. For a deposit of  $30,800 at the end of each year for the next 11 years, with 7% interest.

You will have saved:

         $Future\text{ }value=\ 30,800\times \bigg[\dfrac{(1+0.07)^{11}-1}{0.07}\bigg]$

         $Future\text{ }value=\ 30,800\times 15.7835993=\ 486,134.86$

2.  For a deposit of $33,300 each year, for the same number of years and with the same interest rate.

You will have saved:

       $Future\text{ }value=\ 33,300\times \bigg[\dfrac{(1+0.07)^{11}-1}{0.07}\bigg]$

      $Future\text{ }value=\ 33,300\times 15.7835993=\ 525,593.86$

3. For a deposit of $30,800 each year, but with 11 percent interest, for 11 years.

        $Future\text{ }value=\ 30,800\times \bigg[\dfrac{(1+0.11)^{11}-1}{0.11}\bigg]$

       $Future\text{ }value=\ 30,800\times 19.56143=\ 602,492.04$