Answer:
It should take 5.8 years to reach his goal.
Step-by-step explanation:
In order to solve this question we must use the compounded interest's formula shown below:
M = C*(1 + r/n)^(t*n)
Where M is the final amount, C is the initial amount, r is the interest rate, n is the compound rate and t is the time elapsed in years. Applying the data from the problem we have:
5900 = 4500*(1 + 0.0475/2)^(2*t)
5900 = 4500*(1 + 0.02375)^(2*t)
5900 = 4500*(1.02375)^(2*t)
4500*(1.02375)^(2*t) = 5900
(1.02375)^(2*t) = 5900/4500
(1.02375)^(2*t) = 59/45
log[1.02375^(2*t)] = log(59/45)
2*t*log(1.02375) = log(59/45)
t = log(59/45)/[2*log(1.02375)] = 5.77008
It should take 5.8 years to reach his goal.
