Depreciation and Inflation

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Key Ideas Easy Medium Hard

SL 1.4

$FV = PV \times \left(1 + \dfrac{r}{100k}\right)^{kn}$

What to Remember

A negative percent

Depreciation and inflation use the same solver screen as compound interest.

The percent is negative.

A loss of 18% means I% = −18. P/Y and C/Y are 1 when the change happens once a year.

PV is still negative. The positive FV is the later value.

The booklet formula is the same one, with a negative r.

$FV = PV \times \left(1 + \dfrac{r}{100k}\right)^{kn}$

Which word, which sign

Depreciation is an asset losing a percent of its current value each year. I% is the negative of that percent.

Inflation on cash that earns no interest is the same move. The cash buys less. I% is the negative of the inflation percent.

If the calculator says ERR: DOMAIN, check that PV is negative. Use the (−) key.

Worked example

A laptop is bought for $1,400. It depreciates by 18% each year. Find its value after 4 years.

$r = -18,\ k = 1,\ n = 4$

$FV = 1400 \times \left(1 + \dfrac{-18}{100 \times 1}\right)^{4}$

On the solver, type I% = −18.

N = 4
I% = −18
PV = −1400
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=4, I%=-18, PV=-1400, PMT=0, FV=632.970464 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 632.970464$

To the nearest cent, the value is $632.97.

Easy

One Year of Inflation

The cash earns no interest. I% is the negative of the inflation percent.

Example

$250 is held as cash for 1 year and earns no interest. Inflation is 4%. Find the value of the cash in real terms.

Inflation with no interest is a negative rate. I% = −4.

This is one year of inflation and the cash earns no interest, so N = 1.

N = 1
I% = −4
PV = −250
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=1, I%=-4, PV=-250, PMT=0, FV=240 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 240$

The value in real terms is $240.00.

Answer: $240.00

$80 is held as cash for 1 year and earns no interest. Inflation is 5%. Find the value of the cash in real terms.

Show Answer

Inflation with no interest is a negative rate. I% = −5.

This is one year of inflation and the cash earns no interest, so N = 1.

N = 1
I% = −5
PV = −80
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=1, I%=-5, PV=-80, PMT=0, FV=76 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 76$

The value in real terms is $76.00.

Answer: $76.00

$640 is held as cash for 1 year and earns no interest. Inflation is 2.5%. Find the value of the cash in real terms.

Show Answer

Inflation with no interest is a negative rate. I% = −2.5.

This is one year of inflation and the cash earns no interest, so N = 1.

N = 1
I% = −2.5
PV = −640
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=1, I%=-2.5, PV=-640, PMT=0, FV=624 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 624$

The value in real terms is $624.00.

Answer: $624.00

$1,500 is held as cash for 1 year and earns no interest. Inflation is 6%. Find the value of the cash in real terms.

Show Answer

Inflation with no interest is a negative rate. I% = −6.

This is one year of inflation and the cash earns no interest, so N = 1.

N = 1
I% = −6
PV = −1500
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=1, I%=-6, PV=-1500, PMT=0, FV=1410 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 1410$

The value in real terms is $1,410.00.

Answer: $1,410.00

$75 is held as cash for 1 year and earns no interest. Inflation is 8%. Find the value of the cash in real terms.

Show Answer

Inflation with no interest is a negative rate. I% = −8.

This is one year of inflation and the cash earns no interest, so N = 1.

N = 1
I% = −8
PV = −75
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=1, I%=-8, PV=-75, PMT=0, FV=69 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 69$

The value in real terms is $69.00.

Answer: $69.00

$420 is held as cash for 1 year and earns no interest. Inflation is 1.5%. Find the value of the cash in real terms.

Show Answer

Inflation with no interest is a negative rate. I% = −1.5.

This is one year of inflation and the cash earns no interest, so N = 1.

N = 1
I% = −1.5
PV = −420
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=1, I%=-1.5, PV=-420, PMT=0, FV=413.7 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 413.7$

The value in real terms is $413.70.

Answer: $413.70

Medium

Depreciation

The asset loses the same percent each year. I% is that percent with a negative sign.

Example

A car is bought for $18,000. It depreciates by 12% each year. Find its value after 4 years.

Depreciation is a negative rate. I% = −12.

The value changes once a year for 4 years, so N = 4.

N = 4
I% = −12
PV = −18000
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=4, I%=-12, PV=-18000, PMT=0, FV=10794.51648 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 10794.51648$

To the nearest cent, the value is $10,794.52.

Answer: $10,794.52

A piece of equipment is bought for $8,000. It depreciates by 10% each year. Find its value after 6 years.

Show Answer

Depreciation is a negative rate. I% = −10.

The value changes once a year for 6 years, so N = 6.

N = 6
I% = −10
PV = −8000
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=6, I%=-10, PV=-8000, PMT=0, FV=4251.528 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 4251.528$

To the nearest cent, the value is $4,251.53.

Answer: $4,251.53

A camera is bought for $2,400. It depreciates by 25% each year. Find its value after 3 years.

Show Answer

Depreciation is a negative rate. I% = −25.

The value changes once a year for 3 years, so N = 3.

N = 3
I% = −25
PV = −2400
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=3, I%=-25, PV=-2400, PMT=0, FV=1012.5 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 1012.5$

The value is $1,012.50.

Answer: $1,012.50

A boat is bought for $35,000. It depreciates by 8% each year. Find its value after 5 years.

Show Answer

Depreciation is a negative rate. I% = −8.

The value changes once a year for 5 years, so N = 5.

N = 5
I% = −8
PV = −35000
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=5, I%=-8, PV=-35000, PMT=0, FV=23067.853312 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 23067.853312$

To the nearest cent, the value is $23,067.85.

Answer: $23,067.85

A phone is bought for $900. It depreciates by 30% each year. Find its value after 4 years.

Show Answer

Depreciation is a negative rate. I% = −30.

The value changes once a year for 4 years, so N = 4.

N = 4
I% = −30
PV = −900
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=4, I%=-30, PV=-900, PMT=0, FV=216.09 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 216.09$

The value is $216.09.

Answer: $216.09

A sofa is bought for $4,200. It depreciates by 15% each year. Find its value after 7 years.

Show Answer

Depreciation is a negative rate. I% = −15.

The value changes once a year for 7 years, so N = 7.

N = 7
I% = −15
PV = −4200
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=7, I%=-15, PV=-4200, PMT=0, FV=1346.42377078 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 1346.42377078$

To the nearest cent, the value is $1,346.42.

Answer: $1,346.42

Hard

Several Years of Inflation

Same screen as depreciation. N is the number of years, and I% is negative.

Example

$2,000 is held as cash for 6 years and earns no interest. Inflation is 3% per year. Find the value of the cash in real terms.

Inflation with no interest is a negative rate. I% = −3.

This is 6 years of inflation and the cash earns no interest, so N = 6.

N = 6
I% = −3
PV = −2000
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=6, I%=-3, PV=-2000, PMT=0, FV=1665.94400986 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 1665.94400986$

To the nearest cent, the value in real terms is $1,665.94.

Answer: $1,665.94

$500 is held as cash for 8 years and earns no interest. Inflation is 2% per year. Find the value of the cash in real terms.

Show Answer

Inflation with no interest is a negative rate. I% = −2.

This is 8 years of inflation and the cash earns no interest, so N = 8.

N = 8
I% = −2
PV = −500
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=8, I%=-2, PV=-500, PMT=0, FV=425.38151129 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 425.38151129$

To the nearest cent, the value in real terms is $425.38.

Answer: $425.38

$7,500 is held as cash for 4 years and earns no interest. Inflation is 4.5% per year. Find the value of the cash in real terms.

Show Answer

Inflation with no interest is a negative rate. I% = −4.5.

This is 4 years of inflation and the cash earns no interest, so N = 4.

N = 4
I% = −4.5
PV = −7500
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=4, I%=-4.5, PV=-7500, PMT=0, FV=6238.42200469 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 6238.42200469$

To the nearest cent, the value in real terms is $6,238.42.

Answer: $6,238.42

$1,200 is held as cash for 10 years and earns no interest. Inflation is 1.8% per year. Find the value of the cash in real terms.

Show Answer

Inflation with no interest is a negative rate. I% = −1.8.

This is 10 years of inflation and the cash earns no interest, so N = 10.

N = 10
I% = −1.8
PV = −1200
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=10, I%=-1.8, PV=-1200, PMT=0, FV=1000.68208303 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 1000.68208303$

To the nearest cent, the value in real terms is $1,000.68.

Answer: $1,000.68

$360 is held as cash for 5 years and earns no interest. Inflation is 6% per year. Find the value of the cash in real terms.

Show Answer

Inflation with no interest is a negative rate. I% = −6.

This is 5 years of inflation and the cash earns no interest, so N = 5.

N = 5
I% = −6
PV = −360
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=5, I%=-6, PV=-360, PMT=0, FV=264.20544806 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 264.20544806$

To the nearest cent, the value in real terms is $264.21.

Answer: $264.21

$9,800 is held as cash for 7 years and earns no interest. Inflation is 2.4% per year. Find the value of the cash in real terms.

Show Answer

Inflation with no interest is a negative rate. I% = −2.4.

This is 7 years of inflation and the cash earns no interest, so N = 7.

N = 7
I% = −2.4
PV = −9800
PMT = 0
P/Y = 1
C/Y = 1
PMT: END

TI-84 Plus CE TVM Solver. N=7, I%=-2.4, PV=-9800, PMT=0, FV=8267.51134152 with a solve mark, P/Y=1, C/Y=1, END selected.

Move the cursor to FV. Press ALPHA ENTER.

The calculator shows

$FV = 8267.51134152$

To the nearest cent, the value in real terms is $8,267.51.

Answer: $8,267.51

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