Question

FINAL28 Your child is currently six years old. When he turns 19 you want him to be able to withdraw $14700 per year in order to either travel or go to school for four years. If you are able to earn 6.62% compounded semi-annually for the entire time period, what is the single amount of the deposit three years from now that will ensure that your child is able to do this a. $27 777.49 b. $28 777.49 c. $28 877.49 d. $29 877.49 e. $27 877.49

Answer 1

To ensure your child is able to withdraw $14,700 per year for four years starting when he turns 19, you would need to deposit approximately $27,877.49 three years from now.

Step-by-step explanation:

To find the single amount of the deposit three years from now that will ensure your child is able to withdraw $14,700 per year for four years starting when he turns 19, we can use the formula for compound interest:

$14,700 = X(1 + rac{0.0662}{2})^{2(19-6)}

Simplifying the equation:

$14,700 = X(1 + 0.0331)^{26}

Next, divide both sides of the equation by (1 + 0.0331)^{26} to isolate X:

X = rac{14,700}{(1 + 0.0331)^{26}}

Using a calculator, we can calculate that X is approximately $27,877.49.