SME
Engineering Economics
Time value of money
Use this for “What does $8,000 grow to at 6% a year for 9 years?”, what a future amount is worth today, or the years it takes to grow.
Chart
F(9) ≈ 13,520
This is an example. Type your own values to start a new problem.
$
F
=
$
P
(1
+
%)
(F/P)
Factor (F/P, i%, n)
calculated
(P/F)
Factor (P/F, i%, n)
calculated
Formulas
(
F
P
)
=
(1 +
i
100
)
n
1.6895
=
(1 +
6
100
)
9
(
P
F
)
=
1
(
F
P
)
0.5919
=
1
1.6895
F
=
P
×
((
F
P
))
13,516 = 8,000 × 1.6895
Assumptions
•
i is the interest rate per period, and n counts the same periods (years here).
•
One payment: P now, F at the end of year n.
•
Interest compounds once each period, so each year’s interest earns interest after it.
Step-by-step
WE KNOW
P = $8,000, i = 6%, n = 9 yr
FIND
factor (F/P, i%, n) ((F/P)), factor (P/F, i%, n) ((P/F)), future worth (F)
Step 1 · Find factor (F/P, i%, n): (F/P)
Use (F/P) = (1 + i ÷ 100)ⁿ
Each
year
multiplies
the
amount
by
1
+
i
,
so
n
years
multiply
it
by
(1
+
i
)ⁿ.
(
F
P
)
=
(1 +
6
100
)
9
(
F
P
)
=
(1 + 0.06)
9
(
F
P
)
=
1.06
9
(
F
P
)
=
1.6895
Step 2 · Find factor (P/F, i%, n): (P/F)
Use (P/F) = 1 ÷ ((F/P))
Bringing
money
back
n
years
undoes
carrying
it
forward.
(
P
F
)
=
1
1.6895
(
P
F
)
=
0.5919
Step 3 · Find future worth (F)
Use F = P × ((F/P))
Carry
the
present
worth
forward
n
years.
F
=
8,000
×
1.6895
F
=
about
$13,516
Check
Put the numbers back in. Both sides should match.
1.6895
=
(1 +
6
100
)
9
✓
0.5919
=
1
1.6895
✓
13,516 = 8,000 × 1.6895 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Uniform series: (P/A, i%, n) and (A/P, i%, n)
Use this for “A $30,000 loan at 7% is repaid in 8 equal yearly payments. How much is each payment?”, or what a series of payments is worth today.
Uniform series: (F/A, i%, n) and (A/F, i%, n)
Use this for “$1,500 is deposited at the end of each year for 10 years at 5%. How much is there at the end?”, or the deposit a sinking fund needs.
Arithmetic gradient: (P/G, i%, n)
Use this for “Maintenance costs $3,000 in year 1 and rises $400 a year. At 8%, what are 10 years of it worth today?”
Effective annual rate
Use this for “A loan charges 9% a year compounded monthly. What is the effective annual rate, and what would it be compounded continuously?”