Question

Computation of Effective Interest Rate

On June 30, 2016, Gaston Corporation sold $880,000 of 11% face value bonds for $925,670.41. On December 31, 2016, Gaston sold $370,000 of this same bond issue for $352,804.29. The bonds were dated January 1, 2016, pay interest semiannually on each December 31 and June 30, and are due December 31, 2023.

Required:

Compute the effective yield rate on each issuance of Gaston's 11% bonds. Click here to access the tables to use with this problem. Round your answer to the nearest percentage.

June 30, 2016 issuance:	%
December 31, 2016 issuance:	%

Answer 1

Calculation of Effective Interest rate

June 30, 2016 issuance

Effective interest rate is the rate which equates the issue price and matuarity value of the bonds. Issue price more than matuarity value indicates lower effective rate. Bonds pay interest semiannually. No. of interest periods for the issue of June 30, 2016 issue will be from June 30, 2016 to December 31, 2023 i.e. 15 semiannual periods. So we will consider PV factor for 15 periods. Contractual interest rate for each interest period is 5.5% (11%/2). So we will consider some rate lower than 5.5%. Effective yield for issue on June 30, 2016 is calculated in the following table.

Particulars	Issue on June 30, 2016 (A)	PV factor at 5% for 15 periods (B)	Present Value (A*B)
Interest Amount ($880,000*5.5%)	$48,400	10.379658	$502,375.45
Principal	$880,000	0.4810171	$423,295.05
Total			$925,670.50

Therefore the effective rate for the issue on June 30, 2016 is 10% (5%*2).

December 31, 2016 issuance

Issue price less than matuarity value indicates higher effective rate. Bonds pay interest semiannually. No. of interest periods for the issue of December 31, 2016 issue will be from December 31, 2016 to December 31, 2023 i.e. 14 semiannual periods. So we will consider PV factor for 14 periods. Contractual interest rate for each interest period is 5.5% (11%/2). So we will consider some rate higher than 5.5%. Effective yield for issue on December 31, 2016 is calculated in the following table.

Particulars	Issue on December 31, 2016 (A)	PV factor at 6% for 14 periods (B)	Present Value (A*B)
Interest Amount ($370,000*5.5%)	$20,350	9.2949839	$189,152.92
Principal	$370,000	0.44230096	$163,651.36
Total			$352,804.28

Therefore the effective rate for the issue on December 31, 2016 is 12% (6%*2).