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Help with a loan question.

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nickglyn:
Hey guys. I just need help with part ii) of question b. I know the steps of what to do but my algebra isn't good with these types of questions. Could you show me a worked solution please? Thank you!

jakesilove:

--- Quote from: nickglyn on October 18, 2016, 11:50:34 am ---Hey guys. I just need help with part ii) of question b. I know the steps of what to do but my algebra isn't good with these types of questions. Could you show me a worked solution please? Thank you!

--- End quote ---

Hey! So it's clear that



We want to find the value for n that will completely pay off this loan. As A is the amount due after n repayments, we can just set A to zero! This gives us



Now, we need to sum up the geometric series. We do this using the relationship



I always struggle to figure out how many terms there are. In this case, we know that the first term is 1, the second term is r, the third term is r^2 and so on. Therefore, whatever the power of r is, the term is one more than that! So, since the final term is r^(n-1), there will be n terms.





Expanding gives us






Hope I didn't screw up anything there! Let me know if I can clarify anything :)

nickglyn:
Hey so I just need a few things clarified. Why did you use the geometric sum equation for r<1? Isn't our 1.006? Also I'm not sure where you got -166.66667 from :/ sorry hahah

jakesilove:

--- Quote from: nickglyn on October 18, 2016, 03:32:19 pm ---Hey so I just need a few things clarified. Why did you use the geometric sum equation for r<1? Isn't our 1.006? Also I'm not sure where you got -166.66667 from :/ sorry hahah

--- End quote ---

I didn't use the geometric sum for r<1? That's just the standard geometric sum formula. If you mean why I used 1-r^n instead of r^n-1, the formulas are exactly the same either way, one may just be more convenient depending on the value for r.

The -166.66667 was just simplifying the 1/(1-1.006) in the geometric sum equation :)

RuiAce:

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