Answer:
5.1
Step-by-step explanation:
Compounded Annually:
A=P(1+r)^t
A=P(1+r) Â
t
Â
A=27200\hspace{35px}P=20000\hspace{35px}r=0.062
A=27200P=20000r=0.062
Given values
27200=
27200=
\,\,20000(1+0.062)^{t}
20000(1+0.062) Â
t
Â
Plug in values
27200=
27200=
\,\,20000(1.062)^{t}
20000(1.062) Â
t
Â
Add
\frac{27200}{20000}=
20000
27200
​ Â
=
\,\,\frac{20000(1.062)^{t}}{20000}
20000
20000(1.062) Â
t
Â
​ Â
Â
Divide by 20000
1.36=
1.36=
\,\,1.062^t
1.062 Â
t
Â
\log\left(1.36\right)=
log(1.36)=
\,\,\log\left(1.062^t\right)
log(1.062 Â
t
)
Take the log of both sides
\log\left(1.36\right)=
log(1.36)=
\,\,t\log\left(1.062\right)
tlog(1.062)
Bring exponent to the front
\frac{\log\left(1.36\right)}{\log\left(1.062\right)}=
log(1.062)
log(1.36)
​ Â
=
\,\,\frac{t\log\left(1.062\right)}{\log\left(1.062\right)}
log(1.062)
tlog(1.062)
​ Â
Â
Divide both sides by log(1.062)
5.1116317=
5.1116317=
\,\,t
t
Use calculator
t\approx
t≈
\,\,5.1
5.1
The time it will take for the value of the account to reach
$27,200 is 21.9 years to the nearest tenth of a year.
The amount invested(P) = $20,000
The interest paying rate (R)= 6.2%
The simple interest (SI)= $27,200
Therefore time of interest (T)= X
Using the formula,
SI = P×T×R/100
Make T the subject of formula,
T = SI×100/P×R
T = 27,200× 100/20,000×6.2
T = 2,720,000/124000
T = 21.9 to the nearest tenth of a year.
Learn more about simple interest here:
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