Question

Jacob's college savings are invested in a bond that pays an annual interest of 6.2% compounded continuously. How long will it take for the money to triple?

Answer 1

So you have some initial amount x and we want to know how long it will take with compound interest to triple our original amount x (so 3x). The equation sets up like 3x(the amount we want)= x(original amount) times 1.062(the interest increase)^t So 3x=x(1.062)^t where t is the amount of years. When you divide both sides by x it cancels out and you end up with 3=1.062^t. Take the natural log of both sides. Ln(3) = Ln(1.062^t) and the t being an exponent can come in front of the the natural log. Ln(3) = t(Ln(1.062)) Divide both sides by (Ln(1.062)),. Ln(3)/Ln(1.062)=t. And you should just plug that into a calculator to find t.