Answer:
It will take about 5.5 years (rounded to the nearest tenth) for the savings account to reach $1500 with quarterly compounding at a 5% annual interest rate.
Explanation:
Using the formula for the amount A in the savings account after t years
A = P(1 + r/n)^(nt)
where P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have
P = $1000
r = 5% = 0.05 (decimal)
n = 4 (quarterly compounding)
A = $1500
We want to find the time t that it takes to reach $1500. We can rearrange the formula to solve for t
t = (1/n) * log(A/P) / log(1 + r/n)
Substituting the values we have
t = (1/4) * log(1500/1000) / log(1 + 0.05/4) ≈ 5.5
Hence, it will take about 5.5 years (rounded to the nearest tenth) for the savings account to reach $1500 with quarterly compounding at a 5% annual interest rate.