Question

Mr. Diaz deposits $7000 in an account that earns compound interest. The annual interest rate is 8%, and the interest is compounded twice a year. To the nearest cent, what will the account balance be after 5 years if Mr. Diaz makes no further deposits or withdrawals?

Answer 1

The account balance after 5 years with an 8% annual compound interest rate compounded semi-annually on a $7000 deposit will be $10,361.68 to the nearest cent.

Step-by-step explanation:

To calculate the account balance after 5 years with compound interest, we use the formula A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested or borrowed for, in years.

In Mr. Diaz's case, the principal amount P is $7000, the annual interest rate r is 8% or 0.08, the interest is compounded semi-annually (n = 2), and the time t is 5 years.

Plugging these values into the formula we get:

A = 7000(1 + 0.08/2)^(2*5)

A = 7000(1 + 0.04)^(10)

A = 7000(1.04)^(10)

A = 7000(1.48024)

A = $10,361.68

Therefore, the account balance after 5 years will be $10,361.68 to the nearest cent if no further deposits or withdrawals are made.