Question

How much would you have to deposit into an account with an 8% interest rate, compounded continuously, to have 3000 in your account 10 years later?

Answer 1

So, you would have to deposit approximately $1348.68 into the account to have $3000 in 10 years.

Step-by-step explanation:

To calculate the amount you would have to deposit into an account with an 8% interest rate, compounded continuously, to have $3000 in your account 10 years later, you can use the formula

A = P*e^(rt)

where

• A is the final amount
• P is the principal amount (initial deposit)
• e is the base of the natural logarithm (approximately 2.71828)
• r is the interest rate
• t is the time in years.

Plugging in the values, we get:

A = P * e^(0.08*10)

3000 = P * e^0.8

Now we can solve for P:

P = 3000 / e^0.8

P ≈ 3000 / 2.2255

P ≈ 1348.68

So, you would have to deposit approximately $1348.68 into the account to have $3000 in 10 years.