Question

LIlly deposits $800 into a bank that pays 4.6% annual interest compounded continuously. She uses the formla A=Pe^rt

1. What is the value of R that you would substitute into the Formula? Explain how you got that value.

2. Find the balance in the account after 5 years. Round your answer to the nearest cent.

3 How long will it take the account to reach $1,500? Round your answer to the nearest hundredths.

Answer 1

The value of r that you would substitute into the formula is 0.046, by converting the annual interest rate from a percentage to a decimal. The balance in the account after 5 years is approximately $978.86. It will take approximately 10.83 years for the account to reach $1,500.

Step-by-step explanation:

To find the value of r that you would substitute into the formula A = Pe^rt, we need to use the given information. In this case, the interest rate is 4.6% annually. To convert this into a decimal, we divide it by 100, which gives us 0.046. So, we would substitute 0.046 for r.

To find the balance in the account after 5 years, we can use the formula A = Pe^rt. Given that P = $800 and r = 0.046, we substitute these values into the formula and solve for A. The formula becomes A = 800e^(0.046 * 5). Evaluating this expression gives us A ≈ $978.86.

To find out how long it will take the account to reach $1,500, we need to solve for t in the formula A = Pe^rt. Given that P = $800, r = 0.046, and A = $1,500, we substitute these values into the formula and solve for t. The formula becomes 1,500 = 800e^(0.046 * t). Solving this equation for t gives us t ≈ 10.83 years.

Answer 2

Step-by-step explanation:

1) r is the DECIMAL equivalent of the interest percentage 4.6% = .046 =r

2) A = 800 e^(.046(5)) = $ 1006.88

3) 1500 = 800 e^(.046 *t)

solve for t = 13.67 yrs