Find the ending balance in an account that opens with $6,000, earns 6.5% interest compounded quarterly, and is held for 20 years. (Round your answer to the nearest cent.)

P = Po(1+r)^n.

P = Principal bal. after 20 yrs.

Po = $6,000 = Initial deposit.

r = (6.5%/4)/100% = 0.01625 = Quarterly % rate expressed as a decimal.

n = 4Comp/yr * 20yrs. = 80 Compounding
periods.

Plug the calculated values into the given Eq.

P = $21,786.93.

To find the ending balance in the account, we can use the formula for compound interest:

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

Where:
A = the ending balance
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years

In this case, the principal is $6,000, the annual interest rate is 6.5%, the interest is compounded quarterly (n = 4), and the account is held for 20 years.

First, we need to convert the annual interest rate to a decimal by dividing it by 100:
r = 6.5% / 100 = 0.065

Substituting the given values into the formula, we get:
A = 6000(1 + (0.065/4))^(4*20)

Simplifying this equation, we have:
A = 6000(1.01625)^80

Using a calculator, we can calculate the value inside the brackets: 1.01625^80 ≈ 2.015129

Multiplying this value by the principal, we find:
A ≈ 6000 * 2.015129 ≈ 12,090.75

Therefore, the ending balance in the account, rounded to the nearest cent, is approximately $12,090.75.

To find the ending balance in the account, we can use the formula for compound interest:

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

Where:
A = the ending balance
P = the principal amount (the initial balance of the account)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the money is invested for

In this case, the principal amount (P) is $6,000, the annual interest rate (r) is 6.5% (or 0.065 as a decimal), the interest is compounded quarterly (n = 4), and the money is invested for 20 years (t = 20).

Let's plug in these values and calculate the ending balance:

A = $6,000(1 + 0.065/4)^(4*20)
A = $6,000(1 + 0.01625)^(80)
A = $6,000(1.01625)^(80)

To evaluate this expression, we can use a calculator or a spreadsheet. The ending balance will be rounded to the nearest cent.

Therefore, the ending balance in the account is approximately $19,650.35.