#37. Find the Time Required to Double your Money if it is Compounded Continuously

TL;DR

In order to find the time it takes to double your money with continuous compounding at a 7% interest rate, use the PERT formula.

Transcript

number 37 find the time T in years to double your money if $500 is invested at 7% compounded continuously by choosing the appropriate formula and solving it for T don't forget units okay so the key word in this problem is compounded continuously so whenever you see compounded continuously the formula is the PERT formula so a equals P times e to the... Read More

Key Insights

• 😒 Continuous compounding involves the use of the PERT formula, which considers the effect of compounding interest infinitely often over time.
• ☠️ The PERT formula can be manipulated to find various unknowns, such as the time or interest rate, depending on the given information.
• 😒 To find the time to double an investment in continuous compounding, rearrange the formula and use natural logarithms to solve for the exponent.
• 🖐️ The PERT formula is derived from the concept of exponential growth, where the exponent plays a crucial role in determining the final amount.
• ⌛ Using the appropriate formulas and solving step-by-step, one can find the time to double an investment accurately.
• 🖱️ Calculations involving continuous compounding often require the use of a calculator or computer software due to complex equations.
• 💄 The natural logarithm function (Ln) is used to remove the exponential component from the equation, making it solvable for the desired variable.

Summary & Key Takeaways

• The PERT formula, A = P * e^(RT), helps calculate the final amount (A) after a certain time period, given the initial amount (P), interest rate (R), and time (T).

• In this example, $500 is invested at a 7% compounded continuously to double the money.

• By rearranging the formula and using natural logarithms, the time to double the money is found to be approximately 9.9 years.