Question

Bill wants to give Maria a $500,000 gift in seven years. If money is worth 6% compounded semiannually, what is Maria's gift worth today

Answer 1

Maria's gift worth today is calculated by finding the present value of $500,000, which Bill plans to give her in seven years. Using the formula with a 6% interest rate compounded semiannually, the present value is approximately $320,270.74.

Step-by-step explanation:

To determine what Maria's gift is worth today, we need to calculate the present value of the $500,000 that Bill intends to give Maria in seven years at a 6% interest rate compounded semiannually. We can do so utilizing the formula for present value PV = FV / (1 + r/n)^(nt), where PV is the present value, FV is the future value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

By plugging in the values provided: PV = $500,000 / (1 + 0.06/2)^(2*7), we get PV = $500,000 / (1 + 0.03)^(14).

So, to obtain Maria's present value of the future gift:

PV = $500,000 / (1.03)^14

PV = $500,000 / (1.559913)

PV = $320,270.74 (approx)

Therefore, Maria's gift is worth approximately $320,270.74 today.

Answer 2

PV= $332,528.56

Step-by-step explanation:

Giving the following information:

Future value= $500,000

Number of periods= 7 years

Discount rate= 6% compounded annually

To calculate the present value, we need to use the following formula:

PV= FV/(1+i)^n

PV= 500,000 / (1.06^7)

PV= $332,528.56