Question

You establish an ordinary annuity by depositing $7000 into an account at the end of each year at an annual interest rate of 5% compounded annually. determine the accumulated amount in the annuity after 10 years.

Answer 1

The accumulated amount in an annuity with a $7000 annual payment at a 5% interest rate compounded annually for 10 years is $88,046.

Step-by-step explanation:

The accumulated amount A in an ordinary annuity after n periods can be calculated using the formula:

A = P \times \frac{[(1 + r)^n - 1]}{r} where:

• P is the periodic payment
• r is the interest rate per period
• n is the number of periods

For a $7000 annual payment at a 5% interest rate compounded annually for 10 years:

P = $7000, r = 0.05, n = 10

Substituting these values into the formula:

A = $7000 \times \frac{[(1 + 0.05)^{10} - 1]}{0.05}

which simplifies to:

A = $7000 \times \frac{[(1.05)^{10} - 1]}{0.05}

A = $7000 \times 12.578 = $88,046

Therefore, the accumulated amount in the annuity after 10 years is $88,046.