Question

Sam Long anticipates he will need approximately $227,300 in 14 years to cover his 3-year-old daughter's college bills for a 4-year degree. How much would he have to invest today at an interest rate of 10% compounded semiannually?

A. $88,056.27
B. $98,432.14
C. $99,527.63
D. $101,365.42

Answer 1

To find out how much Sam Long needs to invest today at an interest rate of 10% compounded semiannually, use the formula for compound interest.

Step-by-step explanation:

To find out how much Sam Long needs to invest today, we can use the formula for compound interest:

PV = FV / (1 + r/n)^(n*t)

Where PV is the present value (the amount Sam needs to invest), FV is the future value (the amount Sam needs in 14 years), r is the interest rate (0.10), n is the number of times interest is compounded per year (2 for semiannually), and t is the number of years (14).

Plugging in the values:

PV = 227300 / (1 + 0.10/2)^(2*14) = $98,432.14

Therefore, Sam would need to invest approximately $98,432.14 today.