Answer: x = 8.06 years
Explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited.
t represents the number of years
From the information given,
P = 500
r = 6% = 6/100 = 0.06
n = 1 because it was compounded once in a year.
t = x
Therefore, the exponential equation in terms of x is
A = 500(1 + 0.06/1)^1 × x
A = 500(1.06)^x
If A = $800, then
800 = 500(1.06)^x
800/500 = 1.06)^x
1.6 = 1.06)^x
Taking log of both sides, it becomes
Log 1.6 = log 1.06^x = xlog1.06
0.204 = 0.0253 × x
x = 0.204/0.0253
x = 8.06