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Subtract the inflation percent
A value in real terms compares the change with inflation.
Real percent = given percent − inflation percent.
Interest is a positive given percent. Depreciation is a negative given percent.
Put that real percent in I%, even when it is negative. Then use the solver the same way as compound interest.
This is the approximation used in this section.
After the solver
If the question asks for the value, the positive FV is the answer. Round money to the nearest cent.
If the question asks for the overall percentage change, use the FV from the solver.
The percentage change is
\(\dfrac{FV - \text{original}}{\text{original}} \times 100\%\)
A negative percent is a decrease in real terms.
If the rate changes after the first year, run the solver twice. Round the first FV to the nearest cent, then enter it as a negative PV on the second screen.
Worked example
$2,000 earns 4% annual interest, compounded annually, for 3 years. Inflation is 1.5% per year. Find the value in real terms.
Real percent = interest percent − inflation percent.
\(4 - 1.5 = 2.5\)
I% = 2.5, N = 3, and P/Y = C/Y = 1.
I% = 2.5
PV = −2000
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 2153.78125\)
To the nearest cent, the value in real terms is $2,153.78.
One Year
Interest and inflation both apply for one year. Find the value in real terms.
Real percent = interest percent − inflation percent.
\(6 - 4 = 2\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = 2
PV = −600
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 612\)
The value in real terms is $612.00.
Answer: $612.00
Show Answer
Real percent = interest percent − inflation percent.
\(5 - 3 = 2\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = 2
PV = −250
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 255\)
The value in real terms is $255.00.
Answer: $255.00
Show Answer
Real percent = interest percent − inflation percent.
\(4 - 1.5 = 2.5\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = 2.5
PV = −1800
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 1845\)
The value in real terms is $1,845.00.
Answer: $1,845.00
Show Answer
Real percent = interest percent − inflation percent.
\(3 - 7 = -4\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = −4
PV = −90
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 86.4\)
The value in real terms is $86.40.
Answer: $86.40
Show Answer
Real percent = interest percent − inflation percent.
\(8 - 5 = 3\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = 3
PV = −4200
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 4326\)
The value in real terms is $4,326.00.
Answer: $4,326.00
Show Answer
Real percent = interest percent − inflation percent.
\(2.5 - 2 = 0.5\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = 0.5
PV = −750
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 753.75\)
The value in real terms is $753.75.
Answer: $753.75
Several Years
The interest rate and the inflation rate stay the same each year.
Real percent = interest percent − inflation percent.
\(5 - 2 = 3\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = 3
PV = −2500
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 2813.772025\)
To the nearest cent, the value in real terms is $2,813.77.
Answer: $2,813.77
Show Answer
Real percent = interest percent − inflation percent.
\(6 - 4 = 2\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = 2
PV = −800
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 883.26464256\)
To the nearest cent, the value in real terms is $883.26.
Answer: $883.26
Show Answer
Real percent = interest percent − inflation percent.
\(3 - 4.5 = -1.5\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = −1.5
PV = −3500
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 3101.4007554\)
To the nearest cent, the value in real terms is $3,101.40.
Answer: $3,101.40
Show Answer
Real percent = interest percent − inflation percent.
\(7.5 - 2.5 = 5\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = 5
PV = −1200
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 1608.11476875\)
To the nearest cent, the value in real terms is $1,608.11.
Answer: $1,608.11
Show Answer
Real percent = interest percent − inflation percent.
\(4 - 1 = 3\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = 3
PV = −6400
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 8601.0648278\)
To the nearest cent, the value in real terms is $8,601.06.
Answer: $8,601.06
Show Answer
Real percent = interest percent − inflation percent.
\(2.8 - 3.4 = -0.6\)
Use that percent for I%. A negative result stays negative.
Enter the original amount as a negative PV.
I% = −0.6
PV = −950
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 910.81106094\)
To the nearest cent, the value in real terms is $910.81.
Answer: $910.81
Percentage Change
The solver gives the real future value. Then find the overall percentage change.
Real percent = interest percent − inflation percent.
\(5.5 - 2.5 = 3\)
Use that percent for I%. The solver’s FV is the real value.
I% = 3
PV = −4000
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 4637.0962972\)
The percentage change is
\(\dfrac{FV - \text{original}}{\text{original}} \times 100\%\)
\(= \dfrac{4637.0962972 - 4000}{4000} \times 100\%\)
\(= 15.927\%\)
To 1 decimal place,
\(= 15.9\%\)
The real terms percentage change is
\(15.9\%\)
Answer: \(15.9\%\)
Show Answer
Real percent = interest percent − inflation percent.
\(7 - 3 = 4\)
Use that percent for I%. The solver’s FV is the real value.
I% = 4
PV = −1500
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 1897.97852774\)
The percentage change is
\(\dfrac{FV - \text{original}}{\text{original}} \times 100\%\)
\(= \dfrac{1897.97852774 - 1500}{1500} \times 100\%\)
\(= 26.532\%\)
To 1 decimal place,
\(= 26.5\%\)
The real terms percentage change is
\(26.5\%\)
Answer: \(26.5\%\)
Show Answer
Real percent = interest percent − inflation percent.
\(4 - 1.5 = 2.5\)
Use that percent for I%. The solver’s FV is the real value.
I% = 2.5
PV = −8000
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 8830.503125\)
The percentage change is
\(\dfrac{FV - \text{original}}{\text{original}} \times 100\%\)
\(= \dfrac{8830.503125 - 8000}{8000} \times 100\%\)
\(= 10.381\%\)
To 1 decimal place,
\(= 10.4\%\)
The real terms percentage change is
\(10.4\%\)
Answer: \(10.4\%\)
Show Answer
Real percent = interest percent − inflation percent.
\(5 - 2 = 3\)
Use that percent for I%. The solver’s FV is the real value.
I% = 3
PV = −2200
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 2956.61603456\)
The percentage change is
\(\dfrac{FV - \text{original}}{\text{original}} \times 100\%\)
\(= \dfrac{2956.61603456 - 2200}{2200} \times 100\%\)
\(= 34.392\%\)
To 1 decimal place,
\(= 34.4\%\)
The real terms percentage change is
\(34.4\%\)
Answer: \(34.4\%\)
Show Answer
Real percent = interest percent − inflation percent.
\(3.2 - 4 = -0.8\)
Use that percent for I%. The solver’s FV is the real value.
I% = −0.8
PV = −500
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 468.88180645\)
The percentage change is
\(\dfrac{FV - \text{original}}{\text{original}} \times 100\%\)
\(= \dfrac{468.88180645 - 500}{500} \times 100\%\)
\(= -6.224\%\)
To 1 decimal place,
\(= -6.2\%\)
The real terms percentage change is
\(-6.2\%\)
Answer: \(-6.2\%\)
Show Answer
Real percent = interest percent − inflation percent.
\(9 - 6 = 3\)
Use that percent for I%. The solver’s FV is the real value.
I% = 3
PV = −2750
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 3004.99925\)
The percentage change is
\(\dfrac{FV - \text{original}}{\text{original}} \times 100\%\)
\(= \dfrac{3004.99925 - 2750}{2750} \times 100\%\)
\(= 9.273\%\)
To 1 decimal place,
\(= 9.3\%\)
The real terms percentage change is
\(9.3\%\)
Answer: \(9.3\%\)
First Year, Then a New Rate
Depreciation changes after the first year. Inflation stays the same. Round the final value to the nearest $10.
Real percent = depreciation percent − inflation percent. Depreciation is already a loss, so it is negative.
First year:
\(-18 - 3 = -21\)
Run the solver for that one year. Enter the purchase price as a negative PV.
I% = −21
PV = −18500
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 14615\)
Round that FV to the nearest cent: $14,615.00.
Later years, 5 years:
\(-12 - 3 = -15\)
N = 5. Enter $14,615.00 as a negative PV.
I% = −15
PV = −14615
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 6484.75314219\)
To the nearest $10, the value in real terms is $6,480.
Answer: $6,480
Show Answer
Real percent = depreciation percent − inflation percent. Depreciation is already a loss, so it is negative.
First year:
\(-15 - 2 = -17\)
Run the solver for that one year. Enter the purchase price as a negative PV.
I% = −17
PV = −22000
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 18260\)
Round that FV to the nearest cent: $18,260.00.
Later years, 4 years:
\(-8 - 2 = -10\)
N = 4. Enter $18,260.00 as a negative PV.
I% = −10
PV = −18260
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 11980.386\)
To the nearest $10, the value in real terms is $11,980.
Answer: $11,980
Show Answer
Real percent = depreciation percent − inflation percent. Depreciation is already a loss, so it is negative.
First year:
\(-25 - 4 = -29\)
Run the solver for that one year. Enter the purchase price as a negative PV.
I% = −29
PV = −9600
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 6816\)
Round that FV to the nearest cent: $6,816.00.
Later years, 3 years:
\(-10 - 4 = -14\)
N = 3. Enter $6,816.00 as a negative PV.
I% = −14
PV = −6816
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 4335.357696\)
To the nearest $10, the value in real terms is $4,340.
Answer: $4,340
Show Answer
Real percent = depreciation percent − inflation percent. Depreciation is already a loss, so it is negative.
First year:
\(-10 - 2.5 = -12.5\)
Run the solver for that one year. Enter the purchase price as a negative PV.
I% = −12.5
PV = −14000
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 12250\)
Round that FV to the nearest cent: $12,250.00.
Later years, 6 years:
\(-6 - 2.5 = -8.5\)
N = 6. Enter $12,250.00 as a negative PV.
I% = −8.5
PV = −12250
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 7188.90348652\)
To the nearest $10, the value in real terms is $7,190.
Answer: $7,190
Show Answer
Real percent = depreciation percent − inflation percent. Depreciation is already a loss, so it is negative.
First year:
\(-20 - 3.5 = -23.5\)
Run the solver for that one year. Enter the purchase price as a negative PV.
I% = −23.5
PV = −27500
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 21037.5\)
Round that FV to the nearest cent: $21,037.50.
Later years, 4 years:
\(-12 - 3.5 = -15.5\)
N = 4. Enter $21,037.50 as a negative PV.
I% = −15.5
PV = −21037.5
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 10725.5844019\)
To the nearest $10, the value in real terms is $10,730.
Answer: $10,730
Show Answer
Real percent = depreciation percent − inflation percent. Depreciation is already a loss, so it is negative.
First year:
\(-30 - 2 = -32\)
Run the solver for that one year. Enter the purchase price as a negative PV.
I% = −32
PV = −4800
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 3264\)
Round that FV to the nearest cent: $3,264.00.
Later years, 5 years:
\(-15 - 2 = -17\)
N = 5. Enter $3,264.00 as a negative PV.
I% = −17
PV = −3264
PMT = 0
P/Y = 1
C/Y = 1
PMT: END
Move the cursor to FV. Press ALPHA ENTER.
The calculator shows
\(FV = 1285.70286588\)
To the nearest $10, the value in real terms is $1,290.
Answer: $1,290
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