Please help, i'm so confused!

Question

On January 1, 1990, Emilio deposited $1650 into a savings account paying 6.2% interest, compounded monthly. If he hasn't made any additional deposits or withdrawals since then, and if the interest rate has stayed the same, in what year did his balance hit $3300, according to the rule of 72?On January 1, 1990, Emilio deposited $1650 into a savings account paying 6.2% interest, compounded monthly. If he hasn't made any additional deposits or withdrawals since then, and if the interest rate has stayed the same, in what year did his balance hit $3300, according to the rule of 72?
A. 2001

B. 2002

C. 2000

D. 2003

Answer 1

The balance doubles in t years.

 

The monthly compounding multiplier is (1+.062/12)^12t and this shall equal 2.

 

Taking natural logarithms, 12t(ln1.005166666) = ln 2.

 

Solving for t gives 11.2. This means that more than 11 full years pass until this doubling event occurs, so 1990 + 12 = 2002.  Answer: B

 

Presumably the rule of 72 will yield the same answer. (Said rule is not in my repertoire.)