If $5,000 is invested at 8% annual interest compounded monthly, what is the account balance after 5 years, assuming no additional deposits or withdrawals are made?

Sure, to calculate the account balance after 5 years with a monthly compounded interest, we can use the formula for compound interest which is:

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 (in decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

Given: P = $5000 r = 8% or 0.08 (in decimal) n = 12 (since the interest is compounded monthly) t = 5 years

Substituting these values into the formula, we get:

A = 5000 * (1 + 0.08/12)^(12*5)

Now, calculate the expression in the parentheses:

1 + 0.08/12 = 1.00666667

Then, raise this result to the power of 60 (which is 12*5):

(1.00666667)^60 = 1.488864

Finally, multiply this result by the initial principal amount:

A = 5000 * 1.488864 = $7444.32

So, the account balance after 5 years would be approximately $7444.32, assuming no additional deposits or withdrawals are made.