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  #1  
Old 12-02-2018, 12:12 AM
actuaryxjh actuaryxjh is offline
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Default A very basic question

I have a problem that states:

What deposit made today will provide for a payment of $1000 in 1 year and $2000 in 3 years, if the effective rate of interest is 7.5%?

The solution that it gives is:

PV = 1000v + 2000v^3 at 7.5% = $2540.15
(v = 1.075^(-1))

at first I do not understand how does this solution work, until I do the following:

(PV(1+i) - 1000)(i+i)^2-2000 = 0

and solves for PV actually gets me the above solution PV = 1000v+2000v^3

My question is, how to quickly get the solution without going through the process of the te4dious algebraic expression like me? or is my step necessary?

Thank you~
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Old 12-02-2018, 12:14 AM
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Breadmaker Breadmaker is offline
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Draw a timeline. You'll see that the 1,000 needs 1 year of discounting and 3 years for the 2,000.
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Last edited by Breadmaker; 12-02-2018 at 01:28 AM.. Reason: 1
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Old 12-02-2018, 01:25 AM
Academic Actuary Academic Actuary is offline
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Quote:
Originally Posted by actuaryxjh View Post

My question is, how to quickly get the solution without going through the process of the te4dious algebraic expression like me? or is my step necessary?

Thank you~
You can always use the cash flow work sheet and the NPV function.
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Old 12-02-2018, 01:34 AM
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Ya know, you also just demonstrated that the prospective and retrospective methods are equivalent!
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Old 12-02-2018, 01:35 AM
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Originally Posted by Academic Actuary View Post
You can always use the cash flow work sheet and the NPV function.
once you get familiar with the math, let the calculator do your grunt arithmetic!
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Old 12-02-2018, 10:04 PM
actuaryxjh actuaryxjh is offline
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Thank you for your replying~
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