Final Payment amt: $5K in 5 yrs, $5K in 10 yrs to be paid w/

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golazin

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A debt of $5000 due in five years from now and $5000 due ten years from now is to be repaid by a payment of $2000 in two years, a payment of $4000 in four years, and a final payment at the end of six year. If the interest rate is 2.5% compounded annually, how much is the final payment?
 
golazin said:
A debt of $5000 due in five years from now and $5000 due ten years from now is to be repaid by a payment of $2000 in two years, a payment of $4000 in four years, and a final payment at the end of six year. If the interest rate is 2.5% compounded annually, how much is the final payment?
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What formulas did they give you? What have you tried? How far did you get? Where are you stuck?

Please be complete. Thank you! :D

Eliz.
 
golazin said:
A debt of $5000 due in five years from now and $5000 due ten years from now is to be repaid by a payment of $2000 in two years, a payment of $4000 in four years, and a final payment at the end of six year.
Click to expand...
Tell your teacher that's silly and should be: a debt of $10000 is to be repaid.....
 
What i did so far is:
5000(1.025)^-5+ 5000(1.025)6-10 = 2000(1.025)^-2+ 4000(1.025)^-4+ X (1.025)^-6

I'm looking for X but when i solve the equation I got the wrong answer :(
 
Except for the '6' typo, that looks fine. How did you solve it and what did you get?
 
what solved it like this:

8325.2634= 5527.4313+ X(1.025)^-6
X= (-5527.4313+8325.2634)/5526.5690
= $0.506251 this is what I got while the answer is $3244.63
 
I see. How long ago was it that you last took an algebra class? There is no way that $5526 should be in the denominator.
 
golazin, (1.025)^(-6) = .862296.... ; how did you ever get 5526.5690 ? :shock:
 
Well, ok, but getting 5526.5690 instead of .862296.... sure is something that should make you STOP AND THINK!

I didn't realise it at first (thought the 2 loans were for $5000 each, 5000 + interest @2.5% annual due at maturity),
but I see 5000 is the maturity value of each, hence borrowed was:
5yr loan: 5000 / 1.025^5 = 4419.27
10yr loan: 5000 / 1.025^10 = 3905.99 : so total borrowed = 4419.27 + 3905.99 = 8325.26

You can look at the problem this way:
Code: 
Year 0                                    8325.26
Year 1          208.13                    8533.39 : 8325.26 * .025 = 208.13; got that?
Year 2          213.33   -2000.00         6746.72
Year 3          168.66                    6915.38
Year 4          172.88   -4000.00         3088.26
Year 5           77.21                    3165.47
Year 6           79.13                    3244.60 = final payment amount
Hope that helps you "see" a bit.
 
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