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Here is the statement on the NEST website.

"We take a small percentage of the money going into your pot known as a contribution charge. This amount is 1.8 per cent." They then also charge £15 annually.

I have calculated expected returns using CAPM and want to know in real terms the worth of a retirement pot over 40 years.

How do I write a formula to account for 1.8% per every monthly contribution, £15 annually over 40 years and also control for inflation ?

I am using STATA 13.0 for analysis.

Thank you in advance.

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Let's assume you have total year income I. The inflation rate is R and the growth rate is E every year. The contributed rate deducting 1.8% will be C = 0.982. So, for your account you'll have every year

A = (A + I * 0.982) * (1 + E) / (1 + R) - 15

Let's assume you have annual income in 1000, then for years

1: A = (1000 * 0.982) * (1 + 0.073) / (1 + 0.02) - 15 = 1018.03
2: A = (1018.03 + 1000 * 0.982) * (1 + 0.073) / (1 + 0.02) - 15 = 2088.95
3: A = (2088.95 + 1000 * 0.982) * (1 + 0.073) / (1 + 0.02) - 15 = 3215.52
...
40: A = (121682.84 + 1000 * 0.982) * (1 + 0.073) / (1 + 0.02) - 15 = 129023.60

So, you'll deposit 40 000 and got at the end 129 023.60.

But be careful, economic calculation for so long period could be very incaccurate because of the variation of the inflation rate, growth rate and various risks.

The spreadsheet could be very useful.

More accurate formula

A = A * (1 + E) / (1 + R) + (I * 0.982) * (1 + E/2) / (1 + R) - 15

which assume that annual deposit grows only the half of the year. Thus, the result for 40 years will be 124 576.91.

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You're contributing 98.2% of your contributed amount (deducting 1.8%) each month and at the end of the year, deducting a flat 15 pounds.

The easiest way to do this is to use a spreadsheet. But you're missing some key information. What is your expected growth rate and what is your expected inflation rate? Is this a taxable account where you deduct (for example, 35%) of the growth annually for taxes or is this a non-taxable account?

  • I am ignoring taxation , also assuming the individual buys an annuity. The inflation rate is 2% and expected growth rate is 7.3%. Thanks – anonymous1 Jan 6 '16 at 8:03

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