## How long does it take for an investment to quadruple in value if it is invested at 11% compounded continuously? Type the exact

Question

How long does it take for an investment to quadruple in value if it is invested at 11% compounded
continuously? Type the exact answer as your answer (no decimal approximations).

in progress 0
3 years 2021-08-30T01:39:17+00:00 1 Answers 26 views 0

## Answers ( )

1. Let’s assume we have $100 and an interest rate of 7%. For the$100 to quadruple it means that the future value would be $400. Thus, because we are talking about compounding daily we will set us the equation as follows: 100 * (1+1.07)x = 400 Then we will take 400 and divide it by 100 getting: 1.07X = 4 Now we have encountered a problem where we do not know exponent, so we will use logarithm to calculate such and transform our equation to: Log1.07(4)=X Using our calculator we will find that it takes about 20.4895 days to quadruple the money invested under 7% interest rate compounded daily. 2nd: Using the same$100 but with the rate of 5.5% compounded continuously we will be using A=PERT formula

where:

P (principal) is equal to hypothetical $100 E (e) is a mathematical constant, which is approximately 2.718 R (rate) is the interest rate, in our case it is 5.5% T (time) is the time required for money to grow A (amount) is the final amount desired, which is 4 times larger of$100, thus \$400

We have the following:

400 = 100 * e0.055t

400/100 = e0.055t

4 = e0.055t

Then we will apply natural log to both sides of the equations and get the following:

ln(4) = ln(e0.055t)

Since e is the base of ln(x) the equation simplifies to:

ln(4) = 0.055t

Using the calculator to find ln(4) we are getting:

1.38629 = 0.055t

Lastly find t

t = 1.38629/0.055

t = 25.20535202

Plug the answers back to the original equation to verify the answers.

1st part of the question answer: t = 20.4895

2nd part of the question answer: t = 25.20535202