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Chapter 8: Problem 49

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 ?

Short Answer

Expert verified
The amount parents need to set aside now is calculated by solving the equation from step 3.

Step by step solution

01

Identify the variables

Firstly, identify the variables from the problem statment. The future value \(FV = $80,000\), the child's present age is 5 and education starts at the age of 18, so the time period \(t = 18 - 5 = 13\) years. The interest rate \(r = 6\% = 0.06\) and it is compounded semiannually so \(n = 2\).
02

Substitute the values into the formula

Next, substitute these values into the present value formula \(PV = FV / (1 + r/n)^(nt)\). So, \(PV = 80000/(1 + 0.06/2)^(2*13)\).
03

Calculate the Present Value

Now, simplify the above equation to calculate the present value. This will give us the amount to be set aside right now in order to reach the financial goal when the child turns 18 years old.

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