First Year Accounting for Assets

All of the reports are presented in current year real dollars and show end-of-year balances.

Every model assumes three important variables:

  1. prior end-of-year balance,
  2. inflation rate, and
  3. nominal rate of return.

The prior-year balance, the inflation rate, and the nominal rate of return are entered in the program input areas. These variables are used to calculate end-of-year balance for the Regular Assets and the Retirement Accounts shown in the reports.

There are two equivalent ways of looking at this accounting:

METHOD ONE: Nominal rate of return for all years with all balances expressed in current year real current-year dollars

This example assumes the current year is 2020 and the household starts with a 2019 prior end-of-year balance of $1M and a nominal return of 3% and inflation of 2%.

Year Nominal Rate of Return Prior Amount End-of-Year Balance in Nominal Dollars Inflation End-of-Year Balance in Today's (2020) Dollars
2019     = $1,000,000    
2020 1.03 * $1,000,000 = $1,030,000   = $1,030,000
2021 1.03 * $1,030,000 = $1,060,900 / 1.02^1 = 1.020 = $1,040,098
2022 1.03 * $1,060,900 = $1,092,727 / 1.02^2 = 1.040 = $1,050,295
2023 1.03 * $1,092,727 = $1,125,509 / 1.02^3 = 1.061 = $1,060,592

Year One

The $1,000,000 nominal balance at the end of 2019 grows by the nominal rate of return during 2020, i.e. $1,030,000 = 1.03 * $1,000,000, in current year dollars.

The retirement reports show an end-of-year balance of $1,030,000 assuming there are no contributions or withdrawals.

Regular asset end-of-year balance reporting.

Whereas the nominal return is $1,030,000, this $30,000 return is distributed and reported in two places for regular assets: $10,000 is reported as real return in the Total Income report, and the balance of Saving/Withdraw + what remains is shown as the ending balance for 2020. Were there no saving or withdrawal this ending balance in the Regular Assets report would be $1,020,000, where the other $10,000 is shown in the Total Income report, hence the full $30,000 is accounted for.

Year Two Retirement Assets

The $1,030,000 nominal balance at the end of the current year (2020) grows by the nominal rate of return during the second year, i.e. $1,060,900 = 1.03 * $1,030,000, in 2021 dollars. But, these need to be reported in 2020 dollars, so we divide by inflation of 1.02 to get $1,040,098 in 2020 dollars.

Year Three Retirement Assets

The $1,060,900 nominal balance at the end of 2021 grows by the nominal rate of return during 2022, i.e. $1,092,727 = 1.03 * $1,060,900, in 2022 dollars. But, we want that reported in 2020 dollars, so we divide by inflation of 1.02^2 to get $1,050,295 in 2020 dollars.

And so on for each future year.

METHOD TWO: Nominal rate of return for the first year and real rate of return afterwards.

Year Nominal/Real Rate of Return Prior Amount End-of-Year Balance in Today's (2020) Dollars
2019     $1,000,000
2020 1.03 * $1,000,000 = $1,030,000
2021 1.009804 * $1,030,000 = $1,040,098
2022 1.009804 * $1,040,098 = $1,050,295
2023 1.009804 * $1,050,295 = $1,060,592

Note that the end-of-year balances in real 2020 dollars are exactly the same in both cases!

The real rate of return is calculated in this way:

1 + nominal = (1 +real) * (1 + inflation)

So, 1 + real = (1 + nominal) / (1 + inflation). 1 + real = 1.03 /1.02 = 1.009804. Hence, the real rate of return is 0.9804%.