Complete the table to determine the balance A for $21,000 invested at rater = 5% for t years, compounded continuously.Step 1Write the formula for continuously compounded interest in terms of the principal investment P, the rate r, and time t.A =
Question
Complete the table to determine the balance A for $21,000 invested at rater = 5% for t years, compounded continuously.Step 1Write the formula for continuously compounded interest in terms of the principal investment P, the rate r, and time t.A =
Solution
The formula for continuously compounded interest is given by the equation:
A = P * e^(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.
In this case, P = $21,000 and r = 5% or 0.05 when expressed as a decimal.
So, the formula becomes:
A = 21000 * e^(0.05t)
This is the formula you will use to complete the table for different values of t (time in years).
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