Since we are given that the annual rate 6.35% is compounded quarterly, we know that every quarter (i.e., 3 months) and interest of (6.25/4)% or 1.5625% is given. Therefore, we can write the general equation:

(amount at the end of n quarters)=15000(1+.015625)^n

Plugging in 20,000 for '(amount at the end of n quarters)' and solving for 'n' will give us the number of quarters (3 months) it will take to reach that amount.

20000=15000(1.015625)^n

Solving for n, we get:

n=18.5551 quarters

Since the interest is only given at the end of each quarter, we will round this up to 19 quarters. Therefore the number of months is:

number of months=19*3=57 months

Therefore, it will take 4 years and 9 months.