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|
|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|
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|
|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%.