Final answer:
Option B, which is receiving $35,000 now and $49,000 after seven years, is the better choice. When using the 4.5% compound interest rate to calculate the present value, Option B equals $71,007.35 in today's dollars, surpassing Option A's immediate $70,000 by $1,007.35.
Step-by-step explanation:
To determine which payment option is better in terms of today's dollars, we need to calculate the present value of each option using the given interest rate of 4.5% compounded annually. The formula for the present value of a future sum is PV = FV / (1+r)^n, where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.
For the first option of receiving $70,000 now, the present value is simply $70,000, as there is no need to discount this amount. For the second option, we need to calculate the present value of $35,000 received now and the present value of $49,000 received in seven years. The present value of $35,000 received now is $35,000, and the present value of $49,000 received in seven years is calculated as follows:
Present Value of $49,000 in 7 years = $49,000 / (1+0.045)^7
Now we'll do the calculation:
= $49,000 / (1.045)^7
= $49,000 / 1.360886
= $36,007.35 (rounded to two decimal places)
Adding the present value of the amounts received immediately and in seven years for the second option, we get:
$35,000 + $36,007.35 = $71,007.35
Now, comparing the two options:
- Option A: $70,000 now
- Option B: $71,007.35 in terms of today's dollars
Therefore, Option B, receiving $35,000 now and another $49,000 seven years from now is better by $1,007.35 in terms of today's dollars.