The formula, in one paragraph
Four steps. First, the growth factor: one plus the raise, raised to the years. Second, the future salary: your salary times the growth factor. Third, the real value: the future salary divided by the inflation factor, which is one plus the inflation rate, raised to the years. Fourth, the total earned: each year’s salary added up, year one through the last year. The same factors answer the raise question in reverse: the raise you need is the target divided by your salary, raised to one over the years, minus one.
Step 1: Work out the growth factor
Take one plus the raise and raise it to the years. At the example — a 3% raise over 10 years — the factor is 1.03 to the power of 10, which is 1.3439. That number says pay rises 34.39% over the decade, not 30%, because each raise lands on a bigger salary. The factor is the whole trick: once you have it, every other step is one multiplication or division.
Step 2: Work out the future salary
Multiply your salary by the growth factor. At the example, $65,000 times 1.3439 is $87,354.56. That is the number on the pay slip in 10 years, before tax — the nominal salary. Per month that is $7,279.55, against $5,416.67 today. The nominal gain is $87,354.56 minus $65,000, which is $22,354.56. It looks like a big rise, and it is, until you take the next step.
Step 3: Work out the real value
Divide the future salary by the inflation factor. At the example, 2.5% inflation over 10 years gives an inflation factor of 1.025 to the power of 10, which is 1.2801, so $87,354.56 divided by 1.2801 is $68,241.25. That is what the bigger pay slip actually buys, in today’s money. The real gain is $68,241.25 minus $65,000, which is only $3,241.25. Per month the real pay is $5,686.77. The lesson of the example is right here: a 3% raise against 2.5% inflation is barely a raise at all.
Step 4: Work out the total you earn
Add up each year’s salary. At the example the salaries are $66,950.00 in year one, $68,958.50 in year two, $71,027.26 in year three, $73,158.07 in year four, $75,352.81 in year five, $77,613.40 in year six, $79,941.80 in year seven, $82,340.06 in year eight, $84,810.26 in year nine and $87,354.56 in year ten. Added up they are $767,506.72. In today’s money the total is $667,696.74. The total has no tax taken off and no interest added: it is the gross pay the decade hands you, and it is the number to plan the savings rate against.
How long until you reach $100,000
Divide the target by your salary, take the natural log, and divide by the natural log of one plus the raise. At the example, the natural log of 100,000 divided by 65,000, divided by the natural log of 1.03, is 14.57 years. At a 4% raise it takes 10.98 years, and at a 5% raise it takes 8.83 years. The same rule says your salary doubles in 23.45 years at a 3% raise: the natural log of 2 divided by the natural log of 1.03.
How to find the raise you need
Divide the target by your salary, raise it to one over the years, and subtract one. At the example, 100,000 divided by 65,000 is 1.5385; raised to one tenth it is 1.0440, so the raise you need is 4.40% a year. To reach $80,000 in 10 years you need 2.10% a year, and to reach $150,000 you need 8.72% a year. Or start from the other end: the starting salary that reaches $100,000 in 10 years at a 3% raise is $100,000 divided by 1.3439, which is $74,409.39. That number is the one to compare against a job offer with a lower salary and a bigger raise.
What inflation does to a pay freeze
Run the same steps with a 0% raise. The salary stays $65,000, and the inflation factor is still 1.2801, so the real value is $65,000 divided by 1.2801, which is $50,777.90. A pay freeze is a $14,222.10 pay cut in real terms over 10 years. At 5% inflation a 3% raise is still a cut: the real value is $53,628.13, which is $11,371.87 below today. The rule is simple: if the raise is below inflation, the pay is falling, whatever the pay slip says.
What NOT to do
Do not add the raise ten times and call it 30%: the factor is 1.3439, not 1.30, and the missing 4.39 points are the compounding. Do not compare the nominal salary to today’s prices: $87,354.56 in 10 years buys $68,241.25 of today’s goods, and the $22,354.56 nominal gain is only a $3,241.25 real gain. Do not use one average inflation rate when your own costs run hotter: if your rent and childcare rose 5% while the CPI rose 2.5%, use 5%.
That box is the whole formula.
Worked example: the $65,000 salary
Step 2: $65,000 × 1.3439 = $87,354.56.
Step 3: $87,354.56 ÷ 1.2801 = $68,241.25.
Step 4: $66,950.00 + $68,958.50 + $71,027.26 + $73,158.07 + $75,352.81 + $77,613.40 + $79,941.80 + $82,340.06 + $84,810.26 + $87,354.56 = $767,506.72.
Answer: in 10 years your salary is $87,354.56, worth $68,241.25 today, and the decade earns $767,506.72.