Question

Suppose a friend tells you about an annuity that pays 6% annual interest. You invest in the annuity contributing $10,000 semiannually for 6 years. What is the value of the annuity after your last investment? Enter your answer rounded to the nearest hundred dollars and omit the dollar sign and comma (For example, $42,570.21 should be entered as 42600.)

Answer 1

The future value of the annuity with semiannual contributions of $10,000 at 6% annual interest over 6 years is approximately $79,100, rounded to the nearest hundred dollars.

Step-by-step explanation:

To calculate the future value of an annuity with a semiannual contribution, we can use the future value of an annuity formula: FV = P × ​((1 + r/n)^(nt) - 1) / (r/n), where:

• P represents the semiannual payment amount,
• r is the annual interest rate,
• n is the number of times interest is compounded per year,
• t is the number of years the money is invested for.

In this case, P is $10,000, r is 0.06, n is 2 (semiannual), and t is 6 years.

Plugging the values into the formula gives us:
FV = 10000 × ((1 + 0.06/2)^(2×6) - 1) / (0.06/2)

This results in FV = 10000 × ((1 + 0.03)^(12) - 1) / 0.03. Calculating this, we get a future value of approximately.$79,085.72, which we round to the nearest hundred dollars as required.
The value of the annuity after the last investment is $79,100.