Questions: You have the choice of receiving 100,000 now or 50,000 now and another 70,000 seven years from now. In terms of today's dollar, which choice is better and by how much? Money is worth 4.7% compounded annually.
Which choice is better?
A. The choice of 100,000 now is better
B. The choice of 50,000 now and 70,000 in seven years is better.
C. They are equal in value.
The better choice is greater than the alternative choice by 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.)
Transcript text: You have the choice of receiving $\$ 100,000$ now or $\$ 50,000$ now and another \$70,000 seven years from now. In terms of today's dollar, which choice is better and by how much? Money is worth $4.7 \%$ compounded annually.
Which choice is better?
A. The choice of $\$ 100,000$ now is better
B. The choice of $\$ 50,000$ now and $\$ 70,000$ in seven years is better.
C. They are equal in value.
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.)
Solution
Solution Steps
Step 1: Calculate the Present Value of the Lump Sum Option
The present value of receiving $X now is simply $100000, as it does not need to be discounted.
Step 2: Calculate the Present Value of the Second Option
The present value of the second option is calculated by adding the present value of $Y (which is $Y itself, as it is received immediately) and the present value of $Z, which is calculated using the formula $PV = \frac{Z}{(1 + R)^N} = \frac{70000}{(1 + 0.047)^7}$. Thus, the present value of the second option is $100754.12.
Step 3: Compare the Present Values of Both Options
The present value of the lump sum option is $100000, and the present value of the second option is $100754.12. Therefore, the second option is the better choice.
Step 4: Find by How Much One Option is Better Than the Other
The difference in present value between the two options is $754.12.