How long will it take money to double if it is invested at 4 % compounded continuously?

Name: Problem 33, Chapter 3: Calculus for Business, Economics, Life Sciences, and Social Sciences
Uploaded: 2021-05-14T18:55:18-08:00
Duration: 59 s
Channel: Kaylee Mcclellan
Description: How long will it take money to double if it is invested at 4 % compounded continuously?

step 1 How long will it take an investment to double if it's invested at 4 % compounded continuously? S

How long will it take money to double if it is invested at 4...

Key Concepts

Natural Logarithm

The natural logarithm (denoted as ln) is the logarithm to the base e, where e is an irrational constant approximately equal to 2.71828. It is used to solve equations involving exponential functions, such as those found in continuous compounding, by transforming multiplicative processes into additive ones, making it easier to isolate the variable of interest.

Doubling Time

Doubling time is the period it takes for an investment to grow to twice its initial value. In the context of continuous compounding, it can be determined by setting the final amount equal to two times the principal and solving for t using the exponential growth formula, leading to the equation t = ln(2)/r.

Exponential Growth

Exponential growth occurs when the increase in a quantity is proportional to its current size, resulting in growth that accelerates over time. In financial contexts, continuous compounding is a classic example where the accumulated amount grows exponentially as interest is continuously compounded.

Continuous Compounding

Continuous compounding is a method of calculating interest where the interest is added an infinite number of times per period. It is modeled by the formula A = Pe^(rt), where A is the amount after time t, P is the initial principal, r is the annual interest rate, and t is the time period. This method leads to exponential growth as interest accrues constant accrual over every possible moment.

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