Question

Suppose an initial amount of 100 (deer or dollars, your choice) increases at an annual rate of 7.8%. How long will it take for the amount to double? Round to the nearest 0.01 year.

Answer 1

It will take approximately 9.23 years for the amount to double at a 7.8% annual growth rate, as estimated by the rule of 72.

Step-by-step explanation:

To calculate how long it will take for an initial amount of 100 (whether deer or dollars) to double with an annual interest rate of 7.8%, we can use the rule of 72.

The rule of 72 is a simple way to estimate the number of years required to double the invested money at a given annual rate of return.

According to this rule, we divide 72 by the annual interest rate.

So, our calculation is:

=> 72 ÷ 7.8 = approximately 9.23 years.

Hence, it will take 9.23 years for the initial amount to double at a 7.8% annual growth rate.

This illustration is based on the formula for compound interest, which is also used to calculate growth in various scenarios such as banking, investments, and ecological populations.