Write the formula for continuously compounded interest in terms of the principal investment P, the rate r, and time t.A = $$Pe(rt) Step 2Substitute values for P and r.
Question
Write the formula for continuously compounded interest in terms of the principal investment P, the rate r, and time t.A = Pe(rt) Step 2Substitute values for P and r.
Solution
The formula for continuously compounded interest in terms of the principal investment P, the rate r, and time t is given by:
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).
- e is the base of the natural logarithm, approximately equal to 2.71828.
- r is the annual interest rate (in decimal).
- t is the time the money is invested for, in years.
In the second step, you substitute the given values for P (the principal amount) and r (the annual interest rate) into the formula. For example, if P = $1000 and r = 5% per year, then the formula becomes:
A = 1000 * e^(0.05*t)
This will give you the amount of money accumulated after t years, including interest.
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