9514 1404 393
Answer:
3.67 years
Explanation:
The amount is found using the compound interest formula.
A = P(1 +r/n)^(nt)
for principal P invested at annual rate r compounded n times per year for t years.
We can solve this for t:
A/P = (1 +r/n)^(nt) . . . . divide by P
log(A/P) = (nt)log(1 +r/n) . . . . take the logarithm
t = log(A/P)/(n·log(1 +r/n)) . . . . divide by the coefficient of t
Filling in the given values, we find ...
t = log(12000/10000)/(4·log(1 +0.05/4)) ≈ 3.6692
It will take about 3.67 years for the balance to reach $12,000.