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Diego deposited a certain sum of money in a bank 2 years ago. If the bank had been paying interest at the rate of 8% compounded continuously and he has $13,000 on deposit today, what was his initial deposit? (Round your answer to the nearest cent.)

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Answer:

Diego's initial deposit is $11,111

Explanation:

Let A be the initial deposit Diego made

The amount he will get after two years with continuously compounded interest rate 8% is given by

V = A [tex]e^{rt}[/tex]

Where r is the annual interest rate and t is the number of years (2)

And the actual amount he receive is 13,000

So A = [tex]\frac{V}{e^{0.08\times2} }[/tex] = 13,000 / 1.17 = $11,111

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