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

Every model assumes three important variables:

- prior end-of-year balance,
- inflation rate, and
- 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%.

Year | Nominal Rate of Return | Prior Amount | End-of-Year Balance in Nominal Dollars | Inflation | End-of-Year Balance in Today's (2018) Dollars |
---|---|---|---|---|---|

2017 | = $1,000,000 | ||||

2018 | 1.03 | * $1,000,000 | = $1,030,000 | = $1,030,000 | |

2019 | 1.03 | * $1,030,000 | = $1,060,900 | / 1.02^1 = 1.020 | = $1,040,098 |

2020 | 1.03 | * $1,060,900 | = $1,092,727 | / 1.02^2 = 1.040 | = $1,050,295 |

2021 | 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 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.**

Year | Nominal/Real Rate of Return | Prior Amount | End-of-Year Balance in Today's (2018) Dollars |
---|---|---|---|

2017 | $1,000,000 | ||

2018 | 1.03 | * $1,000,000 | = $1,030,000 |

2019 | 1.009804 | * $1,030,000 | = $1,040,098 |

2020 | 1.009804 | * $1,040,098 | = $1,050,295 |

2021 | 1.009804 | * $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%.