You have the choice of receiving $\$ 80,000$ now or $\$ 38,000$ now and another $\$ 56,000$ six years from now. In terms of today's dollar, which choice is better and by how much? Money is worth $4.3 \%$ compounded annually.
Which choice is better?
A. The choice of $\$ 38,000$ now and $\$ 56,000$ in six years is better.
B. They are equal in value.
C. The choice of $\$ 80,000$ now is better.
The better choice is greater than the alternative choice by $\$ \square$ in terms of today's dollar. (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
Answer
Final Answer: The choice of $38,000 now and $56,000 in six years is better. The better choice is greater than the alternative choice by \(\boxed{1499.29}\) in terms of today's dollar.
Step 1 ：We are given two options: receiving $80,000 now or receiving $38,000 now and another $56,000 six years from now. We are asked to determine which option is better in terms of today's dollar, given that money is worth 4.3% compounded annually.
Step 2 ：To solve this, we need to calculate the present value of the two options and compare them. The present value (PV) is calculated using the formula: \(PV = \frac{FV}{(1 + r)^n}\), where FV is the future value, r is the interest rate, and n is the number of periods.
Step 3 ：For the first option, the present value is simply $80,000.
Step 4 ：For the second option, we need to calculate the present value of $38,000 now and $56,000 six years from now. The present value of $38,000 now is simply $38,000. The present value of $56,000 six years from now is calculated using the formula above with FV = $56,000, r = 4.3%, and n = 6 years.
Step 5 ：After calculating, the present value of the $56,000 received in six years is approximately $43,499.29.
Step 6 ：Therefore, the total present value of the second option (the sum of the present value of $38,000 now and the present value of $56,000 in six years) is approximately $81,499.29.
Step 7 ：Comparing the present values of the two options, we find that the second option is better because its present value ($81,499.29) is greater than the present value of the first option ($80,000).
Step 8 ：The difference between the present values of the two options is approximately $1,499.29.
Step 9 ：Final Answer: The choice of $38,000 now and $56,000 in six years is better. The better choice is greater than the alternative choice by \(\boxed{1499.29}\) in terms of today's dollar.
