Find the number of interest periods to achieve the conditions set forth. A = $6000; P = $1000; interest is 12% compounded quarterly.

15.15 years

Step-by-step explanation:

recall that the formula for compound interest is:

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

where,

A = $6000

P = $1000

r = interest rate = 12% = 0.12

to compound quarterly, n = 4

we are asked to find t

Substituting the above values into the equation:

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

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

6000 = 1000 [ 1 + 0.03 ] ^ (4t)

6000 = 1000 [1.03 ] ^ (4t) (divide both sides by 1000)

6000/1000 = [1.03 ] ^ (4t)

(1.03) ^ (4t) = 6 (applying log to both sides)

log (1.03) ^ (4t) = log 6

4t log (1.03) = log 6

4t = log 6 / log 1.03

t = (log 6 / log 1.03) / 4 (solve with calculator)

t = 15.15 Years