Answer: a) 8.779 years
b) 8.664 years
Step-by-step explanation:
a)
[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]
- A: accumulated amount (balance)
- P: principal amount (original/initial investment)
- r: interest rate (convert to a decimal)
- n: number of times compounded per year
- t: number of years
Given: A = 1800, P = 900, r = 8% = 0.08, n = 3, t = unknown
[tex]1800=900\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\2=\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=ln \bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=3t\ ln\bigg(1+\dfrac{0.08}{3}\bigg)\\\\\\\dfrac{ln\ 2}{3\ ln\bigg(1+\dfrac{0.08}{3}\bigg)}=t\\\\\\\large\boxed{8.779=t}[/tex]
b)
[tex]A=Pe^{rt}[/tex]
[tex]1800=900e^{0.08t}\\\\\\2=e^{0.08t}\\\\\\ln\ 2=0.08t\\\\\\\dfrac{ln\ 2}{0.08}=t\\\\\\\large\boxed{8.664=t}[/tex]
