Question

In financial circles, the “rule of 72” pertains to investing money. It states that dividing 72 by the interest rate gives the time t in years it takes to double the money. Using this rule, what would be the coefficient k for an interest rate of 6%? (Hint: To model the doubling of money, use kt = ln2.)

Answer 1

t=72/6=12

kt=ln2

so k=(ln2)/12

Answer 2

The basic equation is (1+i)^t = 2
Take the natural logarithm, ln, of both sides: tln(1+i) = ln 2 = .693
Thus k= ln (1+i)= ln 1.06 =.0583
And .693/.0583 = 11.887

Answer 3

@nurali the problem is to find k you don't need the last line which is to find t. It's good to know how to derive the formula but for this problem we were told to divide 72 by the interest rate to find t. we already had t and were told to use kt = ln2

Answer 4

k= (ln2)/12 as rulnick already had
ln2/12 = 0.0577 so you also have an error in your computation.

Answer 5

thank you so much. That is right. @triciaal

Answer 6

you are so welcome