Interest problem for a test

Question

If you put 500 dollars in the bank, the interest rate is 1.5, how long until it triples

Answer 1

Hi Great!

The basic form of annual compounding interest is given in the form y=a*(1+r)^t.

A would be the initial money you invested (a=500) and the rate would be the interest but make sure you divide the percent by 100 (r=1.5/100). If we plug the known values so far into the equation, we would get y=500*(1.015)^t. We want to solve for the t (time) variable when our initial value of 500 triples. Multiply 500*3 and plug that into our y variable. 1500=500*(1.015)^t. If we now use order of operations, we would divide the 500 to the other side and that would give us the 3=(1.015)^t. From here, we would use log rules to solve for t. Take the log_(1.015) on both sides to cancel out the 1.015 on the right side and bring the t out as a coefficient. Our resulting equation ends up being log_1.0153=t. Plug that into your calculator and you will get the answer for t. T=74 years