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The formula for calculating the amount of money returned for an initial deposit into a bank account or CD (certificate of deposit) is given by

A is the amount of the return.

P is the principal amount initially deposited.

r is the annual interest rate (expressed as a decimal).

n is the number of compound periods in one year.

t is the number of years.

Carry all calculations to six decimals on each intermediate step, then round the final answer to the nearest cent.

d) If a bank compounds continuously, then the formula used is A = Pe where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the hundredth%26#039;s place.

e)A commonly asked question is, “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth%26#039;s place.

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d) A= Pe^(rt) = 2000*e^(.08*5) = 2983.65

e) double

4000 = 2000 e^(.08 t)

2 = e^(.08t)

ln2 = .08t

ln2/.08 = t

8.66 = t

about 9 years

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Forget about formulas.

If P is put in initially, then every year it grows to

P*(1+r)

So after t years, the amount you have is

P*(1+r)^t

And you want this to be equal to 2P

So (1.08)^t = 2

Take logs

t*ln(1.08) = ln(2)

t = ln(2) / ln(1.08) = 9 years