Question

mike deposited $20000 in a saving account in which interest is compounded continuously. the annual rate of interest is 2.5 %. how much does he have in this account after 18 years?

Answer 1

Mike will have approximately $31,366 in his savings account after 18 years, with an initial deposit of $20,000 and an annual interest rate of 2.5% compounded continuously.

Step-by-step explanation:

To determine how much money Mike will have in his savings account after 18 years when the interest is compounded continuously at an annual rate of 2.5%, we use the formula for continuous compounding:

A = Pert

where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• t is the time in years.

In Mike's case, P = $20000, r = 0.025 (2.5% written as a decimal), and t = 18. Plugging these values into the formula gives us:

A = 20000e(0.025)(18)

Next, we calculate the exponent part using a calculator:

e(0.025)(18) ≈ e0.45 ≈ 1.5683

Then we multiply this by the principal amount:

A = 20000 * 1.5683 ≈ $31366

Therefore, after 18 years, Mike will have approximately $31,366 in his savings account.