Answer: 13.9
(Not-rounded: 13.89561)
Explanation:
A=19200P=10000r=0.0475t=?
n=2\text{ (semi-annually)}
n=2 (semi-annually)
19200=10000(1+\frac{0.0475}{2})^{2t}
19200=10000(1+
2
0.0475
)
2t
19200=10000(1.02375)^{2t}
19200=10000(1.02375)
2t
\frac{19200}{10000}=\frac{10000(1.02375)^{2t}}{10000}
10000
19200
=
10000
10000(1.02375)
2t
1.92=(1.02375)^{2t}
1.92=(1.02375)
2t
\log(1.92)=\log((1.02375)^{2t})
log(1.92)=log((1.02375)
2t
)
\log(1.92)=2t\log(1.02375)
log(1.92)=2tlog(1.02375)
\frac{\log(1.92)}{2\log(1.02375)}=\frac{2t\log(1.02375)}{2\log(1.02375)}
2log(1.02375)
log(1.92)
=
2log(1.02375)
2tlog(1.02375)
t=\frac{0.2833012}{0.0203878}
t=
0.0203878
0.2833012