Nominal and Effective Interest Rates in Engineering Economics, Slides of Engineering Economy

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2/25/ Prepared by: Engr. Emy Barrioquinto

NOMINAL AND EFFECTIVE

INTEREST RATES

ENGINEERING ECONOMICS E N G R. E M Y B A R R I O Q U I N T O

Types of Interest rates

• Nominal Interest Rates – works according to Simple Interest Rates and does not take into accounts compounding periods.
• Effective Interest Rates - caters the compounding periods during a payment plan. It is used to compare the annual interest between loans with different compounding periods like week, month, year etc 2/25/ Prepared by: Engr. Emy Barrioquinto

2/25/ Prepared by: Engr. Emy Barrioquinto

EFFECTIVE INTEREST RATES IN ANNUITY

• IF PP = CP

• IF PP < CP

• IF PP > CP

For example situation period compounding PP = CP Monthly (12) Monthly (12) PP < CP Quarterly (4) Monthly (12) PP > CP Monthly (12) Quarterly (4)

2/25/ MONTHLY DEPOSIT OF 6,000.00 FOR 3 YEARS, WITH INTEREST RATE OF 8% COMPOUNDED MONTHLY. What is the Future worth?

1. Determine the parameters
2. Solve for interest rate per payment period
3. Determine n Prepared by: Engr. Emy Barrioquinto

• IF PP = CP

EFFECTIVE INTEREST RATES IN ANNUITY

2/25/ 6,000 MONTHLY DEPOSIT FOR 3 YEARS, WITH INTEREST RATE OF 8% PER YEAR COMPOUNDED Quarterly.

1. Determine the parameters
2. Solve for interest rate per COMPOUNDING period.
3. Solve base amount by dividing annuity with Interest Period
4. Determine n (based on compounding period) Prepared by: Engr. Emy Barrioquinto

• IF PP > CP

EFFECTIVE INTEREST RATES IN ANNUITY

(1) PP = 12, CP = 4, IP = 1/ (2) Nominal interest rate of 8% - > interest rate per compounding: 0.08/4 = 0. (3) Base amount = 6,000 / (1/3) = 18, (4) n: 3 years * 4 compounding period = 12 Solve future value using this notation 18,000 (F/A, 0.02%, 12)

2/25/ Prepared by: Mr. Juan P. Dela Cruz

EFFECTIVE INTEREST RATES IN ANNUITY

• ‘
• IF PP = CP : solve for interest rate per payment period
• IF PP < CP : solve for effective interest rate per payment period
• IF PP > CP : solve for interest rate per compounding period

Single Amounts

If a nominal interest rate is quoted and the number of compounding periods per year and number of years are known, any problem involving future amounts, annual, or present equivalent values can be calculated by straightforward use of equations 𝐹 = 𝑃 (1+ 𝑖) 𝑁 (Single payment compound amount factor) and 𝑖 = (1 + 𝑟 𝑀 ) 𝑀 − 1, respectively 2/25/ Prepared by: Engr. Emy Barrioquinto

EFFECTIVE INTEREST RATES IN SINGLE FLOW

Single Amounts

2/25/ Prepared by: Engr. Emy Barrioquinto

EFFECTIVE INTEREST RATES IN SINGLE FLOW

When there is more than one compounded interest period per year, the formulas and tables for uniform series and gradient series can be used as long as there is a cash flow at the end of each interest period 2/25/ Prepared by: Engr. Emy Barrioquinto EFFECTIVE INTEREST RATES IN GRADIENT SERIES

Certain operating savings are expected to be 0 at the end of the first six months (period 1 with 6 months), to be $1,000 at the end of the second six months, and to increase by $1,000 at the end of each six-month period thereafter, for a total of four years. Find the equivalent uniform amount, A, at the end of each of the eight six-month periods if the nominal interest rate is 20% compounded semiannually. 2/25/ Prepared by: Engr. Emy Barrioquinto Note that gradient is treated like Annuity

1. Determine the parameters and identify the situation. (this situation is PP = CP)
2. Identify what type of interest to use according to the situation
3. Determine n (based on payment period or compounding)

2/25/ Prepared by: Engr. Emy Barrioquinto Maria wants to save for a new laptop and plans to deposit $500 at the end of each quarter into a savings account that earns a nominal annual interest rate of 8% compounded monthly. She will make these deposits for 3 years. How much will Maria have in her account at the end of 3 years? 𝒊 = 𝟏 + 𝒓 ( 𝑰 𝑷 ) ( 𝑷 𝑷 ) 𝑰 𝑷 − 𝟏

2/25/ Prepared by: Engr. Emy Barrioquinto Which yield better return: a) 9% compounded daily or b) 9.1% compounded monthly?