SME
Grade 9 Math · Problem type
Growth by a percent
Use this for “$800 earns 3% a year, compounded yearly. How much after 4 years?”
Chart
y-intercept (0, 800)
f(4) ≈ 900.407
This is an example. Type your own values to start a new problem.
A
=
P
(1
+
%)
g
Growth factor
worked out (not typed)
Formulas
g
=
1
+
r
100
1.03
=
1
+
3
100
A
=
P
×
g
t
900.41
=
800
×
1.03
4
Assumptions
•
The amount grows by the same percent r each period: it compounds.
•
Write r as a decimal: 3% is 0.03, so the growth factor is 1.03.
•
To find t for a target amount, look along the graph or a table.
Step-by-step
WE KNOW
t = 4, P = $800, r = 3%
FIND
growth factor (g), amount after t years (A)
Step 1 · Find growth factor (g)
Use g = 1 + r ÷ 100
Write
the
rate
as
a
decimal
and
add
it
to
1:
the
amount
is
multiplied
by
g
each
period.
g
=
1
+
3
100
3% = 0.03
g
=
1.03
Step 2 · Find amount after t years (A)
Use A = P × gᵗ
Multiply
the
starting
amount
by
g
once
for
each
period.
A
=
800
×
1.03
4
A
=
800
×
1.1255
A
=
about
$900.41
Check
Put the numbers back in. Both sides should match.
1.03
=
1
+
3
100
✓
900.41
≈
800
×
1.03
4
✓
Topic check
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