Answer:
t = 69.4879 years ≈ 69 years 5 months and 27 days
Explanation:
A = P × [tex](1+\frac{r}{n})^{nt}[/tex]
Here,
A = total amount = $8,000
P = principal or amount of money deposited = $125
r = annual interest rate = 6%
n = number of times compounded per year = monthly i.e 12
t = time in years
thus,
$8,000 = $125 × [tex](1.005)^{12t}[/tex]
or
[tex](1.005)^{12t}[/tex] = 64
taking natural log both the sides, we get
[tex]\ln((1.005)^{12t})[/tex] = ln(64)
or
12t × ln(1.005) = ln(64)
or
12t = [tex]\frac{\ln(64)}{\ln(1.005)}[/tex]
or
12t = 833.85433
or
t = 69.4879 years ≈ 69 years 5 months and 27 days
