Question

Tyrone invested $11,500 in a savings account. If the interest rate is 3.2%, how much will be in the account in 6 years by compounding continuously? Round to the nearest cent.

Answer 1

To find the future value of an investment with continuous compounding, the formula A = Pert is used where P is the principal, e is the base of the natural logarithm, r is the rate, and t is the time. In the given problem, with an initial investment of $11,500 at a 3.2% interest rate for 6 years, the formula needs to be applied and the result rounded to the nearest cent to find the amount after the period.

Step-by-step explanation:

To calculate the future value of an investment with continuous compounding, we use the formula A = Pert, where P is the principal amount, e is the base of the natural logarithm, r is the interest rate as a decimal, and t is the time in years. In Tyrone's case, he invested $11,500 at an interest rate of 3.2% for 6 years.

Using the formula:

1. Convert the interest rate from a percentage to a decimal by dividing by 100: r = 3.2/100 = 0.032.
2. Substitute the values into the formula: A = 11500 * e(0.032*6).
3. Calculate the result using a calculator capable of exponentiation with the natural base e.
4. Round the result to the nearest cent.

After performing the calculation, you will find the amount in the account after 6 years by compounding continuously.