Question

David invested $89,000 in a bank account paying an interest rate of 3.1% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest $10, would be in the account after 15 years?

Answer 1

To calculate the total amount in the bank account after 15 years with continuous compounding, you use the formula A = P*e^(rt) with the given principal amount, interest rate, and time period, and then round the result to the nearest $10.

Step-by-step explanation:

The question involves the concept of compound interest compounded continuously, which is a common topic in high school mathematics. To find the amount of money in the account after 15 years, we'll use the formula for continuous compounding, which is A = P*e^(rt), where:

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

In this scenario, David invested $89,000 at an interest rate of 3.1% (r = 0.031) for 15 years (t = 15). Applying the formula, we get:

A = 89000 * e^(0.031*15)

Using a calculator to evaluate the exponential expression, we can find the total amount A. Rounding to the nearest $10 as requested by the student, we'll provide the final amount of money in the bank account after 15 years.