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JKCPA, CPA

Category: Finance

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Experience: Bachelors degree and CPA with Accounting experience.

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For an Accountant:How do I calculate the Effective Interest

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For an Accountant: How do I calculate the Effective Interest Rate using Table 6-2: Present Value of a Single Sum (for the Principal) and Table 6-4: Present Value of an Ordinary Annuity of 1 (for the Interest) using the trial and error method? Problem: A Company sells 10% bonds having a Maturity Value of $3,000,000 for a carrying value of $2,783,724. The bonds are dated 1/1/2012 and have a maturity date of 5 years. Interest is payable annually on January 1. I do not understand how they arrived at the discounted value of the principal ($1,702,290) and the discounted value of the interest ($1,081,434) to equal the purchase price of $2,783,724.

For the principle, take the discounted value of the principal and divide by the maturity value: 1,702,290 / 3,000,000 = 0.56743. You then search in Table 6-2 for 0.56743. This factor can be found under the 12% column at the 5th period row.

For the interest, the annual interest payment would be 10% x $3,000,000 = $300,000. Then take the discounted value of the interest and divide by the annual interest payment. This is 1,081,434 / 300,000 = 3.60478. In table 6-4, this factor also can be found under the 12% column at the 5th period row.

Therefore, we can state that the effective interest rate is 12%.

The discounted value of the principle can be found by using the formula for the present value of a single sum = Future value x (1 + i)^-n. So this would be $3,000,000 / (1 + 0.12)^5 = 3,000,000 / (1.76234) = 1,702,282 (difference from 1,702,290 is due to rounding).

The discounted value of the interest can be found by using the formula for the present value of an ordinary annuity = interest payment x (1 - (1/(1 + i)^n) / i = $300,000 x (1 - (1/(1+0.12)^5)/0.12 = 300,000 x (1 - (1/1.76234)/0.12) = 300,000 x (1 - 0.56743)/0.12 = 300,000 x (0.43257/0.12) = 300,000 x 3.60475 = 1,081,425 (difference from 1,081,434 is due to rounding).

You can also use the present value formula in Excel to find these amounts if you prefer.

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