Answer:
7 years
Explanation:
A = P (1 + r)^(n)
where A is the final amount, P is the initial amount, r is the interest rate, and n is the number of times of compounding.
Compounded quarterly means compounded 4 times per year. So the effective interest rate per compounding is:
r = 0.07 / 4
r = 0.0175
Given that A = 8000 and P = 5000:
8000 = 5000 (1 + 0.0175)^n
1.6 = 1.0175^n
log 1.6 = n log 1.0175
n = (log 1.6) / (log 1.0175)
n ≈ 27.1
Rounding up to the nearest whole number, it takes 28 compoundings. Since there's 4 compoundings per year:
t = 28 / 4
t = 7
It takes 7 years.