Question

8. Calculate annuity cash flows Aa Aa Your goal is to have $20,000 in your bank account by the end of four years. If the interest rate remains constant at 6% and you want to make annual identical deposits, how much will you need to deposit in your account at the end of each year to reach your goal? $3,657.48 O $3,200.30 O $4,571.85 O $5,486.22 If your deposits were made at the beginning of each year rather than an at the end, by how much would the amount of your deposit change if you still wanted to reach your goal by the end of four years? O $194.09 O $258.79 $219.97 O $323.49

Answer 1

Answer to Question 8.

Answer a.

Desired sum after 4 years = $20,000
Interest rate = 6%

Let annual deposit at the end of each year be $x

$x*1.06^3 + $x*1.06^2 + $x*1.06 + $x = $20,000
$x * (1.06^4 - 1) / 0.06 = $20,000
$x * 4.3746 = $20,000
$x = $4,571.85

So, annual deposit at the end of each year is $4,571.85

Answer b.

Desired sum after 4 years = $20,000
Interest rate = 6%

Let annual deposit at the beginning of each year be $x

$x*1.06^4 + $x*1.06^3 + $x*1.06^2 + $x*1.06 = $20,000
$x * 1.06 * (1.06^4 - 1) / 0.06 = $20,000
$x * 4.6371 = $20,000
$x = $4,313.06

So, annual deposit will decrease by $258.79 ($4,571.85 - $4,313.06)