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#1




Problem
You are given an nyear annuity due of 1 per year plus a final payment at time (n+k1). The present value of the payments can be simplified to (1v^n+k)/d. Calculate the final payment.
Can someone please help me? Thank you. Last edited by Sullinator; 10212018 at 08:41 AM.. 
#2




It would be helpful if you included the possible answers, if it is a sample multiple choice question, and what the source says the answer is.
Also, for the benefit of both you and people who might try to help you, you should start by posting your thoughts about how you might try to solve it. Biggest advantage of that: just documenting your thoughts may alert you to something you’re doing wrong or to how you could go further. Secondary advantage: no one has to document for you steps that you would already be doing on your own. For this question, on reasonable approach (other thought processes would be similar): 1. What is the PV of all the payments except the last payment? 2. By subtracting that from the total PV, what is the PV of the last payment? 3. If that’s the PV of it, how much is the payment? 
#4




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Then calculate the PV of the payments at payments of 1 at time 0, time 1, ..., time n. From that find out how much more you need as the PV of the payment of X. What`s the source of the problem, and was it multiple choice? As an aside (to help you understand why the answer is correct; not necessarily recommended because hard to see why you would do this under exam conditions). Think about a time line with payments of 1 at time 0, time 1, ..., time n, then y at time n+1, n+2, n+k1. Get the PV of all those payments. Compare it to the PV of all the payments in your original series. Figure out how much y would be. Use that to figure out how much the single payment of X must be, to replace those payments of y you don´t get. That’s not a recommended way to solve the problem. It’s just an “ah so” way of seeing why the answer works. 
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