Answer:
40.6 years
Explanation:
A = P (1 + r/n)^nt
whereas
A = final amount
P = the principal amount
r = rate of interest
t = time in years
When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4n = number of times the amount is compounding.
So n = 4
A = P (1 + r/4)^4t
If A is 500,000, P is 20,000, r is 0.08
500000 = 20000(1 + 0.08/4)^4t
25 = (1+ 0.02)^4t
25 = (1.02)^4t
Take the log of both sides
ln 25 = 4t (ln 1.02)
4t = (ln 25)/(ln 1.02) = 162.55
so t = 162.55/4 = 40.6 years