# Effective and Nominal Interest

Very easy effective and nominal interest questions.

I need full solutions for problems 4.6, 4.8, 4.11, 4.15, 4.19, 4.21, 4.30, 4.32, 4.37, 4.45, 4.54, 4.56. (See attached file for full problem description.)

4.6 For an interest rate of 12% per year compounded every 2 months, determine the nominal interest rate per (a) 4 months, (b) 6 months, and (c) 2 years.

4.8 Identify the following interest rate statements as either nominal or effective:

(a) 1.3% per month; (b) 1% per week, compounded weekly; (c) nominal 15% per year, compounded monthly; (d) effective 1.5% per month, compounded daily; and (e) 15% per year, compounded semiannually.

4.11 What nominal interest rate per year is equivalent to an effective 16% per year, compounded semiannually?

4.15 An interest rate of 12% per year, compounded monthly, is equivalent to what nominal and effective interest rates per 6 months?

4.21 A company that specializes in online security software development wants to have $85 million available in 3 years to pay stock dividends. How much money must the company set aside now in an account that earns interest at a rate of 8% per year, compounded quarterly?

4.30 Thermal Systems, a company that specializes in odor control, made deposits of $10,000 now, $25,000 at the end of month 6, and $30,000 at the end of month 9 Determine the future worth (end of year of the deposits at an interest rate 16% per year, compounded quarterly.

4.32 Northwest Iron and Steel is considering getting involved in electronic commerce. A modest c-commerce package is available for $20,000. If the company wants to recover the cost in 2 years, what is the equivalent amount of new income that must be realized every 6 months, if the interest rate is 3% per quarter?

4.37 Fieldsaver Technologies, a manufacturer of precision laboratory equipment, borrowed $2 million to renovate one of its testing labs. The loan was repaid in 2 years through quarterly payments that increased by $50,000 each time. At an interest rate of 3% per quarter, what was the size of the first quarterly payment?

4.45 What effective interest rate per 6 months is equal to a nominal 2% per month, compounded continuously?

4.54 What is the future worth in year 8 of a present sum of $50,000 if the interest rate is 10% per year in years 1 through 4 and 1% per month in years 5 through 8?

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#### Solution Preview

All the text is also in the attached file.

4.6 For an interest rate of 12% per year compounded every 2 months, determine the nominal interest rate per (a) 4 months, (b) 6 months, and (c) 2 years.

The nominal interest rate is not adjusted for compounding, so in this problem, it would be 12% per year. The compounding doesn't matter because we're talking about the nominal rate not the effective rate.

a) The nominal interest rate per 4 months is 12/3 = 4%. (There are three 4 month periods in a year, so divide the annual interest rate by 3.)

b) The nominal interest rate per 6 months is 12/2 = 6%.

c) The nominal interest rate per 2 years is 12*2 = 24%.

4.8 Identify the following interest rate statements as either nominal or effective:

(a) 1.3% per month; (b) 1% per week, compounded weekly; (c) nominal 15% per year, compounded monthly; (d) effective 1.5% per month, compounded daily; and (e) 15% per year, compounded semiannually.

Remember that the nominal interest rate is not adjusted for compounding (it's often called the APR), and the effective interest rate is adjusted for compounding.

a) nominal

b) nominal - it's 1% per week, but it's compounded weekly, so the effective interest rate isn't any different that the nominal interest rate within a given week

c) effective - it says nominal, but since the 15% doesn't include compounding, you will actually earn more than 15%

d) nominal - it says effective 1.5% which means that you will only earn 1.5% per month, not more than that.

e) effective

4.11 What nominal interest rate per year is equivalent to ...

#### Solution Summary

This problem set has many questions involving interest rate, nominal vs. effective interest, and future worth. The solution gives answers to questions 4.6, 4.8, 4.11, 4.15, 4.19, 4.21, 4.30, 4.32, 4.45, and 4.54.

Effective and Nominal Annual Interest

1. What is the effective interest rate if nominal annual interest is 14.8% computed monthly?

2. What is the effective interest rate if nominal annual interest is 12.68% computed continuously?

3. What is the effective interest rate if nominal annual interest is 10.68% computed every 2 months?

4. What nominal annual interest is equivalent to an annual effective interest of 15.5% when computed continuously?

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