Johnny opened a savings account 3 years ago. The account earns 7% interest, compounded continuously. If the current balance is $200.00, how much did he deposit initially? Round your answer to the nearest cent.

Question

Mathematics

Ben Bird

11 January, 05:58

Johnny opened a savings account 3 years ago. The account earns 7% interest, compounded continuously. If the current balance is $200.00, how much did he deposit initially? Round your answer to the nearest cent.

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Answers (1)

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Calderon · Answer 1

Answer: the initial deposit is $162.1

Step-by-step explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

r = 7% = 7/100 = 0.07

t = 3 years

A = $200

Therefore,

200 = P x 2.7183^ (0.07 x 3)

200 = P x 1.234

P = 200/1.234

P = $162.1 to the nearest cent