Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
For interest Compounded continuously
The formula for calculating continuously compounded interest is expressed as
A = Pe^rt
where
A is the final amount after t years
P is the principal or initial amount
r is the interest rate
t is the number of years
From the information given,
final amount = 2 x initial amount
Thus,
A = 2P
r = 13/100 = 0.13
By substituting these values into the formula, we have
2P = Pe^0.13t
Dividing both sides by P, we have
2P/P = P/Pe^0.13t
2 = e^0.13t
Taking the natural log of both sides, we have
ln 2 = ln e^0.13t
Recall the following rules of logarithm
lna^b = blna
lne = 1
Thus, we have
ln 2 = 0.13tln e
ln 2 = 0.13t
0.13t = ln 2
Dividing both sides by 0.13, we have
0.13t/0.13 = ln 2/0.13
t = 5.33
It will take 5.33 years for the investment to double in value.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
