Buffy just put some money into a CD that pays 10.1% interest, compounded monthly. According to the rule of 72, in approximately how many years will she have 4 times the amount of money that she has now?

I think the answer is T = 13.70 or 13 years 9 months

Let the principal be 'x' then the Amount will be 4x.

As the interest is compounded monthly:

Rate of interest = 10.1 % = 10.1 / (100*12) = 0.101/12

Time = 12t

Amount = Principal[1 + Rate/100]

⇒ 4x = x[1 + 0.101/12]¹²t

⇒ 4x/x [1 + 0.008416667]¹²t

⇒ 4 = [1.008416667]¹²t

⇒ log (4) = log[1.008416667]¹²t

⇒ 0.602059991327 = [0.003640014891]¹²t

⇒ 12t = 0.602059991327/0.003640014891

⇒ 12t = 165.400419876

⇒ t = 165.400419876/12

t = 13.78 years or 13 years 9 months.

So, it is about 13 years 9 months she will have 4 times the amount of money.