Question

A family is getting a divorce, and part of the divorce settlement involves setting aside money today for college tuition for their daughter who enters college in 9 years. they estimate that the cost of four years' tuition, food, and lodging at the state university their daughter will attend will be $30,300.

(a) find the lump sum that must be invested at 4% semiannually.

Answer 1

To find the lump sum that must be invested at 4% semiannually for college tuition in 9 years, we can use the future value of a single sum formula.

Step-by-step explanation:

To find the lump sum that must be invested at 4% semiannually, we can use the future value of a single sum formula:

FV = PV(1 + r/n)^(nt)

Where:

FV = Future Value (the amount of money needed in 9 years)

PV = Present Value (the lump sum to be invested today)

r = Annual interest rate (4%, but since it's semiannually compounded, we divide it by 2 to get 2%)

n = Number of compounding periods per year (2, since it's semiannually compounded)

t = Number of years (9)

Plugging in the values, we get:

FV = PV(1 + 0.02)^(2*9)

Now we can solve for PV:

PV = FV / (1 + 0.02)^(2*9)

Substituting the given future value of $30,300, we get:

PV = $30,300 / (1 + 0.02)^(2*9)

Simplifying the calculation:

PV = $30,300 / (1.02)^18

PV = $30,300 / 1.4286

PV ≈ $21,227.30

Therefore, a lump sum of approximately $21,227.30 must be invested at 4% semiannually.