On Abby Ellen's graduation from law school, Abby's uncle, Bull Brady, promised her a gift of $24,000 or $2,400 every quarter for the next 4 years after graduating from law school. If the money could be invested at 6% compounded quarterly, which offer should Abby choose? (p. 319)

To determine which offer Abby should choose, we need to calculate the future value of both options and compare them.

Option 1: Receiving a gift of $24,000
The future value of a lump sum investment can be calculated using the formula: FV = PV(1 + r/n)^(nt)

Where:
PV = Present value (initial investment) = $24,000
r = Annual interest rate = 6% = 0.06
n = Number of times interest is compounded per year = 4 (quarterly compounded)
t = Number of years = 4

FV = 24000(1 + 0.06/4)^(4*4)

Simplifying the equation:

FV = 24000(1 + 0.015)^(16)
FV = 24000(1.015)^(16)
FV ≈ 24000(1.275)

FV ≈ $30,600

Option 2: Receiving $2,400 every quarter for 4 years
Since the payments are made quarterly, we can calculate the future value of an ordinary annuity using the formula: FV = PMT * ((1 + r/n)^(nt) - 1) / (r/n)

Where:
PMT = Payment amount per period = $2,400
r = Annual interest rate = 6% = 0.06
n = Number of times interest is compounded per year = 4 (quarterly compounded)
t = Number of years = 4

FV = 2400 * ((1 + 0.06/4)^(4*4) - 1) / (0.06/4)

Simplifying the equation:

FV = 2400 * (1.015^(16) - 1) / 0.015

FV ≈ 2400 * (1.275 - 1) / 0.015
FV ≈ 2400 * 17.5

FV ≈ $42,000

Comparing the two options, we see that Option 2 has a higher future value, approximately $42,000, compared to Option 1, which has a future value of approximately $30,600. Therefore, Abby should choose Option 2 and receive $2,400 every quarter for the next 4 years after graduating from law school.

To determine which offer Abby should choose, we need to calculate the future value of both options and compare them.

Let's start by calculating the future value of the first option, where Abby receives a gift of $24,000. Since this is a one-time gift, the future value of this option is simply the present value itself:

Future Value = Present Value = $24,000

Now, let's calculate the future value of the second option, where Abby receives $2,400 every quarter for 4 years, and the money is compounded quarterly at a rate of 6%.

To calculate the future value, we will use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate / Number of Compounding Periods)^(Number of Compounding Periods * Number of Years)

Present Value = $2,400
Interest Rate = 6% = 0.06 (as a decimal)
Number of Compounding Periods = 4 quarters in a year
Number of Years = 4

Future Value = $2,400 * (1 + 0.06/4)^(4 * 4)

Calculating this using a calculator or spreadsheet software, we get:

Future Value ≈ $2,400 * 1.015^16 ≈ $2,400 * 1.2834 ≈ $3,080.16

Therefore, the future value of the second option is approximately $3,080.16.

Comparing the two options, we see that the future value of the second option is higher than the future value of the first option. Thus, Abby should choose the second option to receive $2,400 every quarter for 4 years, as it will result in a higher payout due to compound interest.