How much should be invested now at an interest rate of 6.5% per year, compounded continuously, to have $1500 in four years? Do not round any intermediate computations, and round your answer to the nearest cent.
Unitary Method
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![**How much should be invested now at an interest rate of 6.5% per year, compounded continuously, to have $1500 in four years?**
**Do not round any intermediate computations, and round your answer to the nearest cent.**
[Input Box: $___] [Options: X, ⟳, ?]
Explanation: This question involves calculating the present value of an investment with continuous compounding interest. You will need to apply the formula for continuous compounding, 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 (decimal).
- \( t \) is the time the money is invested for, in years.
- \( e \) is the base of the natural logarithm, which is approximately equal to 2.71828.
Given:
- \( A = $1500 \)
- \( r = 6.5\% = 0.065 \)
- \( t = 4 \) years
You need to solve for \( P \):
\[ 1500 = Pe^{0.065 \times 4} \]
\[ P = \frac{1500}{e^{0.26}} \]
Calculate the present value \( P \) without rounding any intermediate computations, and then round the final answer to the nearest cent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dbcbf0b-9123-4a1c-9796-89fa34227664%2Fe1c0410f-d832-486f-90c7-6af3ee649e83%2Fwwl7lum_processed.jpeg&w=3840&q=75)
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