Question

Aaron invested $7,500 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 8 years?

Answer 1

Aaron's account balance would be approximately $8,900 after 8 years, calculated using the continuous compounding formula.

Step-by-step explanation:

To determine the future balance of an investment with continuous compounding, we can use the formula for continuous compounding, which is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (as a decimal), and t is the time in years. Here, Aaron's principal amount, P, is $7,500, the annual interest rate, r, is 1.5% or 0.015 when expressed as a decimal, and the time, t, is 8 years.

Using the formula, the future balance is calculated as follows:

A = 7500 * e(0.015*8)

After solving the equation with continuous compounding, we find that the amount of money in Aaron's account to the nearest hundred dollars, after 8 years, is approximately $8,900. This shows the effect of compound interest and how it can grow an investment over time.

Answer 2

\text{Compounded Continuously:}

Compounded Continuously:

A=Pe^{rt}

A=Pe

rt

P=7500\hspace{35px}r=0.015\hspace{35px}t=8

P=7500r=0.015t=8

Given values

A=7500e^{0.015(8)}

A=7500e

0.015(8)

Plug in

A=7500e^{0.12}

A=7500e

0.12

Multiply

A=8456.22638685

A=8456.22638685

Use calculator (with e button)

A\approx 8500

A≈8500

Round to nearest hundred dollars

Step-by-step explanation: