Question

Parents wish to have $80,000 available for a child's education. If the child is now 5 years old, how much money must be set aside at 6% compounded semiannually to meet their financial goal when the child is 18?

Answer 1

Answer: $27,602.60

Step-by-step explanation:

if the kid is 5 years old, there are 13 years left until he is 18.

Now, suppose that the parents set aside an amount A of money in the account.

As the interest is compounded semiannually is compounded two times per year.

The equation that models this situation is:

M(n) = A*(1 + p/(c*100%))^(c*n)

where:

n is our variable, in this case, years.

p is the percentage, in this case, 6%

n is the number of compounds in one unit of the variable, in this case, we have 2.

A is the initial amount, this is the thing we want to find.

Then our equation will be:

M(n) = A*(1 + 6%/(2*%100))^(2*n)

       = A*(1 + 0.03)^(2*n) = A*(1.03)^(2n)

And we want that this is equal to $80,000 when n = 13 (remember that when n = 13, the child will be 18 years old)

M(13) = A*(1.03)^(2*18) = $80,000

           A = $80,000/((1.03)^(2*18)) = $27,602.60

Then they should deposit $27,602.60 now to meet their financial goal when the child is 18.