Question

Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.) $1,800 is deposited quarterly for 20 years at 4% per year FV = $ 172,605.32 .

Answer 1

To find the amount accumulated in the annuity account, use the formula for compound interest. In this case, the amount accumulated after 20 years is $172,605.32 for quarterly deposits of $1,800 at a 4% annual interest rate.

Step-by-step explanation:

To find the amount accumulated in the annuity account, we can use the formula for compound interest:

FV = P(1+r/n)^(n*t)

Where:

• FV is the future value (amount accumulated)
• P is the regular deposit amount (in this case, $1,800)
• r is the interest rate per period (4% per year, or 0.04)
• n is the number of compounding periods per year (quarterly deposits, so n=4)
• t is the number of years (20 years)

Using this formula:

FV = $1,800 * (1 + 0.04/4)^(4*20)

Calculating this expression gives us:

FV = $172,605.32

Therefore, the amount accumulated in the annuity account after 20 years is $172,605.32.