A=$6000; p=$1000; interest is 12% compounded quarterly

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P (1+r/n) ^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1000

r = 12% = 12/100 = 0.12

n = 4 because it was compounded 4 times in a year.

A = 6000

Therefore,.

6000 = 1000 (1+0.12/4) ^4 * t

6000/1000 = (1 + 0.03) ^4t

6 = 1.03^4t

Taking log of both sides of the equation, it becomes

Log 6 = log 1.03^4t

0.778 = 4tlog 1.03

0.778 = 4t * 0.0128

0.778 = 0.0512t

t = 0.778/0.0512

t = 15.2 years