Investments How long, to the nearest year, will it take an investment to t...

Investments How long, to the nearest year, will it take an investment to triple if it is continuously compounded at 10% per year? HINT [See Example 3.]

Example 3:

Global bonds sold by Mexico are yielding an average of 5.2% per year.* At that interest rate, how long will it take a $1,000 investment to be worth $1,500 if the interest is compounded monthly?

Solution Substituting A = 1,500, P = 1,000, r = 0.052, and m = 12 in the compound interest equation gives

and we must solve for t. We first divide both sides by 1,000, getting an equation in exponential form:

In logarithmic form, this becomes

We can now solve for t:

Thus, it will take approximately 7.8 years for a $1,000 investment to be worth $1,500.