Question

I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!

Answer 1

Answer: a) 8.779 years

               b) 8.664 years

Step-by-step explanation:

a)

$A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}$

• 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

$1800=900\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\2=\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=ln \bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=3t\ ln\bigg(1+\dfrac{0.08}{3}\bigg)\\\\\\\dfrac{ln\ 2}{3\ ln\bigg(1+\dfrac{0.08}{3}\bigg)}=t\\\\\\\large\boxed{8.779=t}$

b)  

$A=Pe^{rt}$

$1800=900e^{0.08t}\\\\\\2=e^{0.08t}\\\\\\ln\ 2=0.08t\\\\\\\dfrac{ln\ 2}{0.08}=t\\\\\\\large\boxed{8.664=t}$