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

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.