Answer: 3.3 Years
Step-by-step explanation:
To find the time it takes for a $2900 investment to earn $300 interest at 7% compounded monthly, use the formula
�
=
�
(
1
+
�
/
�
)
�
�
A=P(1+r/n)
nt
, where A = P + $300, P = $2900,
�
=
0.07
r=0.07, and
�
=
12
n=12.
Solve for
�
t, the time in years:
2900
(
1
+
0.07
/
12
)
12
�
=
2900
+
300
2900(1+0.07/12)
12t
=2900+300
(1+0.07/12)12�=
1.10345
(1+0.07/12)
12t
=1.10345
�≈in(
1.10345)12ln
(1+0.07/12)t≈
12ln(1+0.07/12)
ln(1.10345)
Therefore, it would take approximately 3.3 years for the investment to earn $300 interest.
