# Geometric sequences

## Homework Statement

A mortgage is taken out for £80,000. It is to be paid by annual instalments of 5000with the first payment being made at the end of the first year that the mortgage was taken out. Interest of 4% is then charged on any outstanding debt. Find the total time taken to pay off the mortgage.

Sn=a(r^n-1)/r-1

## The Attempt at a Solution

I have no idea here can someone please point me in the right direction, thanks!

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## Homework Statement

A mortgage is taken out for £80,000. It is to be paid by annual instalments of 5000with the first payment being made at the end of the first year that the mortgage was taken out. Interest of 4% is then charged on any outstanding debt. Find the total time taken to pay off the mortgage.

Sn=a(r^n-1)/r-1

## The Attempt at a Solution

I have no idea here can someone please point me in the right direction, thanks!
Since you want a pointer in the right direction, start with your 80K subtract the payment 5K...then add to what remains 4% interest, then subtract 5K again and add to what remains 4% interest, then subtract...and so on. (so long as you don't actually calculate anything here you should see that you'll be summing up terms in a geometric sequence)
Clearly if you keep repeating this process the debt will become zero. the n in your relevant equation is the number of times interest gets added.
For what value of n will it be true that your above summation will be equal to zero?

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I'm getting just over 12 years, is that correct?

it dosen't sound right

with no interest, paying 5000/year. it would take 80000/5000 = 16 years to pay it off. it's going to be more than that with interest

I'm getting just over 12 years, is that correct?
what expression did you form to get that?
furthermore, shouldn't your sum equation be of the form: Sn = (r^(n+1)-1)/(r-1)?

Hmm..am I right in saying that you got 12 years by the following process:
1.a): 80000-5000
1.b): (1.a) - 0.04*(1.a)
1.c): (1.b) - 5000
1.d): (1.c) - 0.04*(1.c)...and so on?

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