Question

When the market rate of interest was at an annual rate of 12%, King company issued $5,000,000, 10-year, 11% bonds payable. The interest on the bonds is to be paid semi-annually.

1. Calculate the selling price of the bonds

2. Calculate the interest expense for the first period using the effective interest method

3. Calculate the interest expense for the first period using the straight line method

As additional security for the bondholders, King has agreed to make ten annual sinking fund deposits of $325,000. The deposits will be made at the end of each year into an account paying 9% annual interest.

How much money will being in the fund at the end of the ten years?

Answer 1

Solution :

1. Selling price of bonds = Interest payment×[1-(1+i)^-n]/ i + Redeemable value/(1+i)ⁿ

= $5 million×5.5%×[1-(1+0.12/2)^10*2 /(0.12/2) + $5,000,000/(1+0.12/2)^10*2

= $275,000×[1-(1.06)²⁰]/0.06 + $5,000,000/ (1.06)²⁰

= 3,154,228.33 + $1,559,023.63

= $4,713,251.97 or $4,713,252 (Rounded off to the nearest dollar)

2. Computation of Interest expense for the first year using effective int. method:

Thus, Interest expense for the first semiannual  period = $282,796 (Rounded off)

And total for the first year = $566,058 (rounded off)

3. Interest expense for the first period using straight-line method = $5 million ×5.5%= $275,000

and total for the first year = 275,000 * 2 = $550,000

Money will be in the fund at the end of 10 year = Future value of annual deposit of $325,000 at the end of 10 year

= $325,000×[(1+i)ⁿ -1)] / i

= $325,000×[(1+0.09)¹⁰ - 1] / 0.09

= $4,937,702.16 (Rounded off to the 2 decimal places)