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 2018 dollars

This example assumes the current year is 2018 and the household starts with a 2017 prior end-of-year balance of \$1M and a nominal return of 3% and inflation of 2%.

YearNominal Rate of ReturnPrior AmountEnd-of-Year Balance in Nominal DollarsInflationEnd-of-Year Balance in Today's (2018) Dollars
2017= \$1,000,000
20181.03* \$1,000,000= \$1,030,000= \$1,030,000
20191.03* \$1,030,000= \$1,060,900/ 1.02^1 = 1.020= \$1,040,098
20201.03* \$1,060,900= \$1,092,727/ 1.02^2 = 1.040= \$1,050,295
20211.03* \$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 2017 grows by the nominal rate of return during 2018, 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/Dis-saving + what remains is shown as the ending balance for 2018. 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 (2018) grows by the nominal rate of return during the second year, i.e. \$1,060,900 = 1.03 * \$1,030,000, in 2019 dollars. But, these need to be reported in 2018 dollars, so we divide by inflation of 1.02 to get \$1,040,098 in 2018 dollars.

Year Three Retirement Assets

The \$1,060,900 nominal balance at the end of 2019 grows by the nominal rate of return during 2020, i.e. \$1,092,727 = 1.03 * \$1,060,900, in 2020 dollars. But, we want that reported in 2018 dollars, so we divide by inflation of 1.02^2 to get \$1,050,295 in 2018 dollars.

And so on for each future year.

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

YearNominal/Real Rate of ReturnPrior AmountEnd-of-Year Balance in Today's (2018) Dollars
2017\$1,000,000
20181.03* \$1,000,000= \$1,030,000
20191.009804* \$1,030,000= \$1,040,098
20201.009804* \$1,040,098= \$1,050,295
20211.009804* \$1,050,295= \$1,060,592

Note that the end-of-year balances in real 2018 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%.