Complete the table to determine the balance A for $10,000 invested at rate r = 4% for t years, compounded continuously. (Round your answers to two decimal places.)t 1 10 20 30 40 50
Question
Complete the table to determine the balance A for $10,000 invested at rate r = 4% for t years, compounded continuously. (Round your answers to two decimal places.)t 1 10 20 30 40 50
Solution
The formula for continuous compounding is 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.
Given P = $10,000 and r = 4% = 0.04, we can calculate A for each value of t:
- For t = 1 year, A = 10000 * e^(0.04*1) = $10,416.86
- For t = 10 years, A = 10000 * e^(0.04*10) = $14,918.58
- For t = 20 years, A = 10000 * e^(0.04*20) = $22,306.47
- For t = 30 years, A = 10000 * e^(0.04*30) = $33,534.34
- For t = 40 years, A = 10000 * e^(0.04*40) = $50,339.41
- For t = 50 years, A = 10000 * e^(0.04*50) = $75,646.23
So, the completed table is:
t 1 10 20 30 40 50 A 14,918.58 33,534.34 75,646.23
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