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Ologhai Jones

Effective Aer Calculation

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£50 per month paid for 10 years. Maturity value: £8,000.

How does one go about working out the effective AER for that? Any ideas? :)

This cannot be done algebraicly (in other words, there is no simple formula for this). The technique involves building the sum of the compound interest on each payment from the day it is deposited, and then performing an iterative search for the interest rate that will yield the correct outcome.

In this case, you should be able to use an APR loan calculator, as the technique is essentially the same.

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Something like this in Excel http://spreadsheets.about.com/od/excelfunctions/qt/20071023_pmt_fv.htm

Will give you a chance of trying different rates iteratively. To see what rate gives you 8000 after 120 x 50.

Or my rule of thumb for interest on loans,

120 x 50 = 6000

Gain = 2000= 33% of investment

X 2 = 66%

/ 10 = 6.6%

So my guess is that it's around that figure, give or take.

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Thanks, both. I feel a bit better knowing that the answer's not too obvious (and, indeed, that there isn't a simply formula).

Presumably, this is the sort of thing:

=PMT(POWER(1.05612, 1 / 12) - 1, 120, 0, -8000, 1)

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Thanks, both. I feel a bit better knowing that the answer's not too obvious (and, indeed, that there isn't a simply formula).

Presumably, this is the sort of thing:

=PMT(POWER(1.05612, 1 / 12) - 1, 120, 0, -8000, 1)

you forgot to add the BBS constant.

Banker Bull Shine

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Thanks, both. I feel a bit better knowing that the answer's not too obvious (and, indeed, that there isn't a simply formula).

Presumably, this is the sort of thing:

=PMT(POWER(1.05612, 1 / 12) - 1, 120, 0, -8000, 1)

That low? 5.6%?

It's like it's ******ing random

http://www.thisismoney.co.uk/money/saving/article-1633419/Monthly-lump-sum-savings-calculator.html gives 5.557%

5.7% on this to get £8k after 10 years at £50pm

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I'm going to give this a go.

£50 per month. 120 payments = n. MER (monthly equivalent rate) = x

r= 1+ x/100

Total value of payments made with compound interest = 50 * (1-r^(n+1)) / (1-r) (Short solution to the sum of a finite geometric series)

Solve (1-r^121) / (1-r) = 8000/50 = 160

Can be done using a Newton-Rapheson iterative search method, or by trial and error. I get r = 1.00447 approx.

Convert to AER

a = (r^12 -1) * 100

AER = 5.79%

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I'm going to give this a go.

£50 per month. 120 payments = n. MER (monthly equivalent rate) = x

r= 1+ x/100

Total value of payments made with compound interest = 50 * (1-r^(n+1)) / (1-r) (Short solution to the sum of a finite geometric series)

Solve (1-r^121) / (1-r) = 8000/50 = 160

Can be done using a Newton-Rapheson iterative search method, or by trial and error. I get r = 1.00447 approx.

Convert to AER

a = (r^12 -1) * 100

AER = 5.79%

I've blindly incorporated your formulas into a spreadsheet that allows the iterative trial-and-error method of finding the effective AER. Blindly because I don't think I have the wherewithal to check your arithmetic!

Thanks for taking the time to present a method.

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  • 239 Brexit, House prices and Summer 2020

    1. 1. Including the effects Brexit, where do you think average UK house prices will be relative to now in June 2020?


      • down 5% +
      • down 2.5%
      • Even
      • up 2.5%
      • up 5%



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