Question

Calculate the amount of money you will have in the bank after 10 years if you deposit $18,000 into a savings account that pays 5% interest compounded continuously. Round your answer to the nearest cent.

Answer 1

After 10 years, by depositing $18,000 in a bank account with a 5% interest rate compounded continuously, you will have approximately $29,676.96.

Step-by-step explanation:

To calculate the amount of money you will have in a bank after 10 years if you deposit $18,000 into a savings account with a 5% interest rate compounded continuously, you use the formula for continuous compounding interest, which is A =
`Pe^(rt)`, where:

• P is the principal amount (the initial amount of money)
• r is the annual interest rate (in decimal form)
• t is the time the money is invested for
• e is the base of the natural logarithm (approximately equal to 2.71828)
• A is the amount of money accumulated after n years, including interest.

For this scenario:

• P = $18,000
• r = 0.05 (5% as a decimal)
• t = 10 years

Substituting these values into the formula gives us:

A =
`18000 *e^(0.05 * 10)` = 18000 *
`e^(0.5)`

Using a calculator to find
`e^(0.5)`, we get:

A = 18000 * 1.64872 (approximately)

A = $29,676.96

Therefore, after 10 years, you will have approximately $29,676.96 in the bank account. This amount is rounded to the nearest cent as requested.