Investments How long will it take a $500 investment to be worth $700 if it is continuously compounded at 15% per year? (Give the answer to two decimal places.) 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.
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