At the beginning of 2015, Laura Company issued 10-year bonds with a face value of $4,000,000 due on December 31, 2020. The company will accumulate a fund to retire these bonds at maturity. It will make ten annual deposits to the fund beginning on December 31, 2015. How much must the company deposit each year, assuming that it will earn 12% interest compounded annually?

Question

Quizplus · Accepted Answer

To calculate the amount the company must deposit each year, we need to find the present value of the amount required to retire the bond at maturity. 
Using the formula:
Present Value = Future Value / (1 + r)^n
where Future Value = $4,000,000, r = 12%, and n = 10 (the number of years left until maturity).
Present Value = $4,000,000 / (1 + 0.12)^10 = $1,051,233.03
Now, we can use the formula for the present value of an annuity to find the annual deposit required:
Annual Deposit = Present Value / ((1 - (1 + r)^-n) / r)
Annual Deposit = $1,051,233.03 / ((1 - (1 + 0.12)^-10) / 0.12) = $227,936.65, which is closest to choice B.

At the Beginning of 2015, Laura Company Issued 10-Year Bonds