Question

Solve each continous exponential growt (h)/(d)ecay A savings account balance is compounded continuously. If the interest rate is 3% per year and the current balance is $1,767.00, what will the balance be 10 years from now?

Answer 1

To find the future balance of an account with continuous compound interest at a 3% annual rate on a principal of $1,767 after 10 years, use the formula A = Pe^(rt), giving a result of approximately $2385.47.

Step-by-step explanation:

Continuous Compound Interest Calculation

To calculate the future balance of an account with continuous compound interest, you can use the formula A = Pert, where:

• P is the principal amount (the initial amount of money)
• r is the annual interest rate (in decimal form)
• t is the time in years

In your case, the principal amount P is $1,767, the annual interest rate r is 0.03 (3% converted to decimal), and the time t is 10 years.

Plugging these values into the formula gives us:

A = 1767 * e0.03 * 10

Using a calculator to evaluate the exponent and multiply by the principal gives us the future balance:

A ≈ 1767 * e0.3

A ≈ 1767 * 1.34986

A ≈ $2385.47

Therefore, the balance of the savings account 10 years from now will be approximately $2385.47.