Question

What savings rate from real income (Spreadsheet 21.3) will produce the same retirementannuity as a 15% savings rate from nominal income?

Short answer

8.3%

Step-by-step solution

Definition of Nominal Income

An income that is not adjusted for changes in purchasing power is known as nominal income.

Calculation of savings rate

Retirement Years	Income growth	Rate of inflation	Savings rate	ROR
25	0.07	0.03	0.083	0.06	0.0291
Age	Income	Defactor	Savings	Cumulative savings	rConsumption 0.0291
30	50,000	1.00	4145	8000	45,855
31	53,500	1.03	4568	17040	47,505
35	70,128	1.16	6739	65769	54,680
45	1,37,952	1.56	17816	329450	77,111
55	2,71,372	2.09	47099	10,06,376	1,07,114
65	5,33,829	2.81	124516	26,21,352	1,45,463
	74,45,673		13,03,467	Retirement annuity	49,668

Calculation of saving rate:

$\begin{array}{rcl}\text{Saving rate}& =& \frac{\text{Savings}}{\text{Total income}}\times 100\\ & =& \frac{4145}{50,000}\times 100\\ & =& 8.29\%\text{or 0.083}\end{array}$

The above calculation shows that a savings rate of 8.3% from real income would yield the desired retirement annuity.