question in the description

Question

2) Daniel deposits $8,000 into a continuously compounding interest account. After 18 years there is $13,006.40 in the account. What was the interest rate?

3)An account has $26,000 after 15 years. The account received 2.3 percent interest compounded continuously. How much was deposited initially?

Use the equation  to answer each question. Show all your work.

Answer 1

A(t) = Pe^rt

1. A = amount after t (=8) years = $13,006.40
2. P = principle = $8000
3. e = Euler's number (it's on your calculator)
4. r = interest rate expressed as a decimal
5. t = time = 8 years

A = Pe^rt

13,006.40 = 8000e^r8

13,006.4/8000 = e^r8

ln(13,006.40/8000) = 8r

(1/8) ln(13,006.40/8000) = r

Use your calculator to get the answer. It will be a decimal value. Convert to a percent.

2) A(t) = Pe^rt

26,000 = Pe^(0.023)(15)

26,000/e^3.45 = P

Use your calculator to get the answer. The units are $$. Round to two decimal places.