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 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 x | $1,000,000 | = $1,030,000 | = $1,030,000 | |
| 2021 | 1.03 x | $1,030,000 | = $1,060,900 | / 1.02^1 = 1.020 | = $1,040,098 |
| 2022 | 1.03 x | $1,060,900 | = $1,092,727 | / 1.02^2 = 1.040 | = $1,050,295 |
| 2023 | 1.03 x | $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%.