Answer:
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
