Use a calculator to help solve the problem.If $600 is deposited in an account paying 8.1% annual interest, compounded continuously, how long will it take for the account to increase to $800? (Round your answer to one decimal place.) yr
Question
Use a calculator to help solve the problem.If 800? (Round your answer to one decimal place.) yr
Solution
To solve this problem, we will use the formula for continuous compound interest, which is A = Pe^(rt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- t is the time the money is invested for, in years.
We know that A = 600, and r = 8.1% or 0.081 (in decimal form). We want to find t.
So, we will rearrange the formula to solve for t:
t = ln(A/P) / r
Substitute the given values into the formula:
t = ln(800/600) / 0.081
Now, use a calculator to compute the value of t. Remember to round your answer to one decimal place.
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