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Calculate AER on NS&I Index Linked Savings

HowardG
HowardG Posts: 2 Newbie
in Savings & investments
I'm hoping someone can provide the calculation that tells me the AER I have earned on my maturing 3 year NS&I Index Linked Savings. Whilst I understand fully the point that the investment is "RPI + 1.15% AER" for three years, I now want to understand at the end of the term the overall actual AER so that I can compare it to having had the money in the bank. I have talked with NS&I and they cannot help (which surprised me as I thought many people must ask this, but they said that "no-one asked").

Also, the fact that it is an NS&I investment is irrelevant as the answer will just be a mathematical calculation which includes compound interest.

So, here are the numbers: In January 2007 I invested £15,000 for 3 years. That has now matured as £16,709.39, so it has grown £1,709.39.

How do I calculate the annual AER I have earned?

Many thanks
Howard

Comments

  • Mr_Mumble
    Mr_Mumble Posts: 1,758 Forumite
    (cube root of £16,709.39/£15,000) * 100 - 1 = 3.6628% AER
    "The state is the great fiction by which everybody seeks to live at the expense of everybody else." -- Frederic Bastiat, 1848.
  • HowardG
    HowardG Posts: 2 Newbie
    Brilliant, thank you so much.

    Howard
  • Etccarmageddon
    Etccarmageddon Posts: 877 Forumite
    Part of the Furniture 500 Posts Name Dropper
    very clever
  • david78
    david78 Posts: 1,654 Forumite
    edited 19 January 2010 at 6:45PM
    Mr_Mumble wrote: »
    (cube root of £16,709.39/£15,000) * 100 - 1 = 3.6628% AER

    The answer given by Mr Mumble is correct, but the formula should be

    (cube root of (£16,709.39/£15,000) - 1)*100 = 3.6628% AER

    I think he just formatted it wrong when he typed it in.

    Still clever though :T
  • Mr_Mumble
    Mr_Mumble Posts: 1,758 Forumite
    Of course I got the 1 and 100 the wrong way round on purpose to test y'all :o
    (I have an ugly habit of just treating both 1 & 100 as mere formatting formalities).

    The basic compound interest formula for the accumulation of capital is:

    FV = PV (1 + r) ^ n

    FV: Future Value.
    PV: Present Value
    r: return
    n: number of time periods

    so to resolve r:

    16,709.39 = 15,000 (1 + r) ^ 3

    16,709.39 / 15,000 = (1 + r ) ^ 3

    3 √ (16,709.39 / 15,000) = 1 + r

    (3 √ (16,709.39 / 15,000)) -1 = r

    r = ( 3 √ 1.1139593 ) - 1

    r = (1.036628) - 1

    r = 0.036628 and then multiply by 100 for a percentage.

    e&oe!
    "The state is the great fiction by which everybody seeks to live at the expense of everybody else." -- Frederic Bastiat, 1848.
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