Chapter 4.6® - Nominal to Effective Interest Rate Calculations & Practice Questions #8 - #16

• Part 4.1 - Time Value of Money, Future Values of Compounding Interest, Investing for more than 1 Period & Examination of Original Investment & Growth of Investment
• Part 4.2 - Compounding Interest Homework Problem & Time Value of Money Continued - Future Value Formula, Growth of $100 & Future Value Comparisons
• Part 4.3 - How to Use a Financial Calculator BAII Plus to Perform Time Value of Money & Present / Future Value Calculations
• Part 4.4 - Changing Advanced Function Keys (BGN, C/Y, P/Y), Converting from Nominal Interest to Effective Interest Rates using BAII Financial Calculator
• Part 4.5 - Examples of Interest Rate Calculations & Practice Questions #1 - #7
• Part 4.6 - Nominal to Effective Interest Rate Calculations & Practice Questions #8 - #16
• Part 4.7 - Present Value & Discounting – We Know the Future Value, how do we find the Present Value? Single Period Case & PV Discounting for Multiple Periods
• Part 4.8 - An Example of Present Value Discounting & Saving Up Money & Deriving the Basic Present Value Equation
• Part 4.9 - Determining the Discount Rate using Basic Present Value equation & Finding the Number of Accounting Periods
• Part 4.10 - Summary of Time Value Formulas & Calculations
• Part 4.11 - Discounted Cash Flow Valuations - Future Value of Multiple Cash Flows & Designing the Cash Flows Timeline
• Part 4.12 - Compound the Accumulated Balance Forward One Year at a Time - Discounted Cash Flow Valuation - Determining Present Value of Multiple Future Cash Flows & Designing a Financial Timeline
• Part 4.13 - Determining Present Value of Multiple Future Cash Flows – Homework Example
• Part 4.14 - Calculating Present Value with Multiple Future Cash Flows – Example #2
• Part 4.15 - Valuing Annuity Level Cash Flows – Present & Future Value of Annuities
• Part 4.16 - Calculating Annuity Payments using Annuity Present Value Factor – Example
• Part 4.17 - Accounting for Perpetuities & Using the Annuity Present Value Factor Formula
• Part 4.18 - Accounting for Growing Perpetuities & Simplified Formula for Present Value of Growing Perpetuity - Example of Growing Perpetuity on Rental Cash Flows

Question:

10% compounded semi-annually is equivalent to what effective rate?

Answer:

i) Press 2nd, and then press 2

ii) NOM = Press 10, Enter then

iii) EFF= Press

iv) C/Y = Press 2, then Enter, then

v) EFF = Press CPT

vi) Answer = 10.25%

9. Question

7.5% compounded annually is equivalent to what effective rate?

Answer:

i) Press 2nd, and then press 2

ii) NOM = Press 7.5, Enter then

iii) EFF= Press

iv) C/Y = Press 1, then Enter, then

v) EFF = Press CPT

vi) Answer = 7.5%

10. Question

9% compounded monthly is equivalent to what effective rate?

Answer:

i) Press 2nd, and then press 2

ii) NOM = Press 9, Enter then

iii) EFF= Press

iv) C/Y = Press 12, then Enter, then

v) EFF = Press CPT

vi) Answer = 9.38%

11. Question

9% compounded quarterly is equivalent to what effective rate?

i) Press 2nd, and then press 2

ii) NOM = Press 9, Enter then

iii) EFF= Press

iv) C/Y = Press 4, then Enter, then

v) EFF = Press CPT

vi) Answer = 9.31%

12. Question

A deposit of $1,500 grows to $4262.04 in 7 years. If the interest is compounded quarterly, what is the effective rate?

Answer:

Note that this 15.2% is a nominal interest rate. What is the effective rate?

i) Press 2nd, and then press 2

ii) NOM = Press 15.2, Enter then

iii) EFF= Press

iv) C/Y = Press 4, then Enter, then

v) EFF = Press CPT

vi) Answer = 16.09%

13. Question

A deposit of $1300 earns $339.45 interest in 3 years. If the interest is compounded monthly, what is the effective rate?

Answer:

Note that this 7.76% is a nominal interest rate. What is the effective rate?

i) Press 2nd, and then press 2

ii) NOM = Press 7.76, Enter then

iii) EFF= Press

iv) C/Y = Press 12, then Enter, then

v) EFF = Press CPT

vi) Answer = 8.04%

Present Value Homework Question

i) An investor requires $25,000 in 7 years and bank offers him 6.76% effective interest rate based on monthly compounding. What amount must he deposit now to achieve his goal?
Note: We recommend you try this problem on your calculator on your own before looking at the solution below, the only way you will learn is if you practice on your own!

On your BA II plus financial calculator

i) Press 2nd, and then press 2

ii) NOM press

iii) EFF= Press 6.76, Enter then

iv) C/Y = Press 12, then Enter, then

v) NOM = Press CPT

vi) Answer = 6.56%

Now we will use this 6.56% in our present value calculation below:

Future Value to Determine Number of Periods Question

An investor has $15,000 and wishes it to grow to $80,000 in the future. If the interest rate is 10% compounded quarterly, how long will this goal take?
Note: We recommend you try this problem on your calculator on your own before looking at the solution below, the only way you will learn is if you practice on your own!