Answer:
10.1 years.
Step-by-step explanation:
It is given that,
Principal = 9000
Rate of interest = 5%
No. of times interest compounded = 2 times in an year
Amount after certain time = 14800
The formula for amount:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where, P is principal, r is rate of interest, n is no. of times interest compounded in an year and t is time in years.
Substitute the given values in the above formula.
[tex]14800=9000(1+\frac{0.05}{2})^{2t}[/tex]
[tex]\frac{14800}{9000}=(1+0.025)^{2t}[/tex]
[tex]1.644=(1.025)^{2t}[/tex]
Taking log both sides.
[tex]\log(1.644)=\log(1.025)^{2t}[/tex]
[tex]\log(1.644)=2t\log(1.025)[/tex] [tex][\because \log a^b=b\log a][/tex]
[tex]\frac{\log(1.644)}{2\log(1.025)}=t[/tex]
[tex]t=10.066[/tex]
[tex]t=10.1[/tex]
Therefore, the required time is 10.1 years.
Answer:
9.4
Step-by-step explanation:
The correct answer is actually 9.4. Delta Math corrected me afterwards.
