At the beginning of 2017,Denero Company issued 10-year bonds with a face value of $4,000,000 due on December 31,2027.The company will accumulate a fund to retire these bonds at maturity.It will make ten annual deposits to the fund beginning on December 31,2017.How much must Denero deposit each year to achieve this investment goal,assuming that it will earn 12% interest compounded annually?
A)$203,515
B)$226,009
C)$227,937
D)$363,636

Question

Quizplus · Accepted Answer

To determine the required annual deposit, we need to calculate the present value of the bond's future value. Using the formula for present value of a lump sum, we get:

PV = FV / (1 + i)n
PV = $4,000,000 / (1 + 0.12)10
PV = $1,064,758.63

This means that in order to accumulate $4,000,000 by the bond's maturity date, Denero needs to deposit $1,064,758.63 in a fund earning 12% annually. To calculate the required annual deposit, we can use the formula for present value of an annuity:

PV = PMT * [1 - (1 + i)-n] / i

Solving for PMT, we get:

PMT = PV * i / [1 - (1 + i)-n]
PMT = $1,064,758.63 * 0.12 / [1 - (1 + 0.12)-10]
PMT = $227,936.72

Therefore, Denero must deposit $227,936.72 each year to accumulate enough funds to retire the bonds at maturity. The closest option to this value is choice C: $227,937.

At the Beginning of 2017,Denero Company Issued 10-Year Bonds with a Face