Question

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.)

Answer 1

Diego's initial deposit is $11,111

Step-by-step 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
`e^(rt)`

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 =
`(V)/(e^(0.08*2) )` = 13,000 / 1.17 = $11,111