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For an Accountant:How do I calculate the Effective Interest

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.

Hi,

Thanks for the question.

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%.

Hope this helps!
Customer: replied 3 years ago.

How do you first find the discounted value of the principal? How do you then find the discounted value of the interest?

Your answer was very helpful but I am not sure of the above. Can you further assist me? Thank you.

Hi,

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.

Customer: replied 3 years ago.

Thank you for your additional effort. I will be putting this information to good use shortly. Thanks again.

You're welcome. I hope this helps. When you are ready, please take a moment to rate my service. I'd appreciate it as this is the only way I can receive credit for my work. Thanks!!!