Actuarial Outpost A very basic question
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 Financial Mathematics Old FM Forum

#1
12-02-2018, 01:12 AM
 actuaryxjh SOA Join Date: Aug 2018 College: Rutgers University Posts: 6
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~
#2
12-02-2018, 01:14 AM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 3,689

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 02:28 AM.. Reason: 1
#3
12-02-2018, 02:25 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,338

Quote:
 Originally Posted by actuaryxjh 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.
#4
12-02-2018, 02:34 AM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 3,689

Ya know, you also just demonstrated that the prospective and retrospective methods are equivalent!
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#5
12-02-2018, 02:35 AM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 3,689

Quote:
 Originally Posted by Academic Actuary 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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#6
12-02-2018, 11:04 PM
 actuaryxjh SOA Join Date: Aug 2018 College: Rutgers University Posts: 6