Question

Aubree invested $8,300 in an account paying an interest rate of 2.2% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 13 years?

Answer 1

Aubree will have $10,870.22 in her account after 13 years, to the nearest cent, by investing $8,300 at 2.2% interest compounded quarterly.

Step-by-step explanation:

To calculate the future value of an investment with compound interest, we use the formula:

A = P(1 + r/n)^(nt), where:

• A is the amount of money that will be in the account after n years.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal form).
• n is the number of times that interest is compounded per year.
• t is the number of years the money is invested.

For Aubree's investment of $8,300 at 2.2% interest compounded quarterly for 13 years, the calculation is done as follows:

• First, convert the interest rate from a percentage to a decimal by dividing by 100: 2.2% / 100 = 0.022.
• Since the interest is compounded quarterly, n will be 4.
• Now, we can just plug the numbers into the formula: A = 8300(1 + 0.022/4)^(4*13).

Calculating this out, it comes to:

A = 8300(1 + 0.0055)^(52)

A = 8300(1.0055)^(52)

A = 8300 * (1.309677).

Aubree will have $10,870.22 in her account after 13 years, to the nearest cent.

Answer 2

A≈11039.41

Step-by-step explanation:

Plug in values

A=8300(1.0055)^{52}

A=8300(1.0055)

52

Simplify

A=11039.4131948

A=11039.4131948

Round)

A≈11039.41