QuestionSuppose you win a small lottery that pays you $\$ 250$ every month for the next 6 months.
Further suppose that your personal beliefs are such that you believe the discount rate of future sums of money is $10 \%$.
At month \#6, what will that final payment of $\$ 250$ be worth to you under your current financial perspective on the time value of money?

Studdy Solution
Apply the formula to calculate the present value of the final payment.
Given: - $FV = \$250$ - $r = 10\% \text{ per annum} = \frac{10\%}{12} \text{ per month} = 0.00833$ - $n = 6 \text{ months}$
Substitute these values into the formula:
$$PV = \frac{250}{(1 + 0.00833)^6}$$
Calculate the denominator:
$$(1 + 0.00833)^6 \approx 1.05127$$
Now calculate the present value:
$$PV = \frac{250}{1.05127} \approx 237.78$$
Therefore, the present value of the final payment of \$250 at month #6 is approximately:
$\boxed{237.78}$