If the nominal interest rate is zero, then the present discounted value of a sequence of future payments is: Group of answer choiceszero undefined equal to the last of the payments equal to the sum of all payments equal to the square of the sum of all payments
Question
If the nominal interest rate is zero, then the present discounted value of a sequence of future payments is: Group of answer choiceszero undefined equal to the last of the payments equal to the sum of all payments equal to the square of the sum of all payments
Solution
The correct answer is "equal to the sum of all payments".
Here's why:
The present discounted value (PDV) of a future payment is calculated as the payment amount divided by (1 + interest rate) raised to the power of the number of periods until the payment is received.
If the nominal interest rate is zero, the formula simplifies to just the payment amount, because anything divided by 1 remains the same, and anything raised to the power of 0 is 1.
Therefore, the PDV of each future payment is just the payment amount itself.
So, if you have a sequence of future payments, the PDV of the whole sequence is the sum of the PDVs of each payment. Since the PDV of each payment is just the payment amount itself, the PDV of the whole sequence is the sum of all payments.
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