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.
