A woman invests $5500 in an account that pays 6% interest per year, compounded continuously.

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Use the formula for continuously compounded interest: A = Pe^(rt) Where: A = final amount P = principal amount r = interest rate t = time in years So: A = 5500e^(0.06*2) A = 6201.23 Now, you want to find t when A = 11,000: 11,000 = 5500e^(0.06t) Divide by 5500: 2 = e^(0.06t) Take the natural log of both sides and simplify: ln(2) = ln(e^(0.06t)) ln(2) = 0.06t ln(2)/0.06 = t 11.55 = t So it will take 11.55 years. For the next question, use the formula for non-continuously compounded interest: A = P(1 + r/n)^(nt) Where: A = final amount, after t years P = principal amount r = interest rate n = number of times compounded yearly t = time, in years So: 6000 = 3000(1 + 0.065/4)^(4t) 2 = 1.01625^(4t) ln(2) = ln(1.01625^(4t)) ln(2) = 4t * ln(1.01625) ln(2)/(4*ln(1.01625)) = t 10.75 = t So, it will take 10.75 years to reach $6000.

can please highlight answer

11.55 = t So it will take 11.55 years.

For the next question, use the formula for non-continuously compounded interest:

10.75 = t So, it will take 10.75 years to reach $6000.

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Use the formula for continuously compounded interest: A = Pe^(rt) Where: A = final amount P = principal amount r = interest rate t = time in years So: A = 5500e^(0.06*2) A = 6201.23 Now, you want to find t when A = 11,000: 11,000 = 5500e^(0.06t) Divide by 5500: 2 = e^(0.06t) Take the natural log of both sides and simplify: ln(2) = ln(e^(0.06t)) ln(2) = 0.06t ln(2)/0.06 = t 11.55 = t So it will take 11.55 years.

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