The money returned to the owners of capital for use of their capital. Compound interest is the result of reinvesting interest, rather than paying it out. Quotation of interest rates

1. Interest
Why Engineers should know ?
Dr. K. Shahzad Baig
Memorial University of Newfoundland (MUN) Canada

2. Interest
“Interest is the money returned to the owners of capital for use of
their capital.”
“When a person loans money, a charge is made for the use of
these borrowed funds.”
“The compensation paid for the use of borrowed capital.”
The size of the fee will depend upon:
i. the scarcity of money, the size of the loan,
ii. the length of the loan,
iii. the risk the lender feels that the loan may not be paid back, and
iv. the prevailing economic conditions.

3. Why Engineers should know about interest ?
Engineers may be involved in the evaluation of an investment of
money in a venture, it is important that they understand the time
value of money and how it is applied in the evaluation of
projects.

4. Types of Interests
Principal: The amount of capital on which interest is paid.
Rate of interest: The amount of interest earned by a unit of
principal in a unit of time.
The time unit is usually taken as one year.

5. Simple Interest
This form of interest requires compensation payment at a
constant interest rate based only on the original principal.
If P represents the principal, N the number of time units or
interest periods, and i the interest rate based on the length of one
interest period, the amount of simple interest I during N interest
periods is
I=P i N
The principal must be repaid eventually; therefore, the entire
amount of principal plus simple interest due after N interest
periods is
F= P+I= P (1+i N )

6. Problem Statement
An initial loan of $1000 at an annual interest rate of 10 percent
would require payment of $100 as interest at the end of the first
year. If this payment were not made, the interest for the second
year would be ?
The total compound amount due after 2 years would be ?
The interest for the second year =
= ($1000 + $100X0.10) = $110
The total compound amount due after 2 years =
= $1000 + $100 + $110 = $1210

7. Problem Statement
Rs. 100,000 was deposited in a bank account and Rs115,000 is
withdrawn one year later.
Compute
a) the interest received from the Rs100,000 investment, and
b) the annual interest rate which was paid
a)
I = Rs. 115,000 – Rs. 100,000 = Rs. 15,000
𝑖 =
15,000/𝑦𝑟
100,000
𝑥 100% = 15% 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟

8. Compound interest
It is the interest calculated on the initial principal and also on the
accumulated interest of previous periods of a deposit or loan, in
other words, interest on interest.
Compound interest is the result of reinvesting interest, rather than
paying it out, so that interest in the next period is then on the
principal sum plus previously accumulated interest.
𝐹 = 𝑃 1 + 𝑖 𝑁
F = The total amount of money accumulated
P = Present Value of Money
i = interest rate
n = Number of interest periods

9. Problem Statement
• At a 10% per year interest rate, how much is $500 now
equivalent to three years from now?
• $500 now will increase 10% in each on the three years
Now End of 1st yr End of 2nd yr End of 3rd yr
$500 500+ 10% (500) 550 + 10% (550) 605 + 10 % (605)
550.00 605.00 665.50
The $500 now is equivalent to $665.50 at the end of 3 years.

10. The time standard for interest computations – One Year
• One Year: Can be segmented into:
– 365 days
– 52 Weeks
– 12 Months
– One quarter: 3 months – 4 quarters/year
• Interest can be computed more frequently than one time a
year
Common Compounding Frequencies

11. Quotation of Interest Rates
Interest rates can be quoted in more than one way.
• Example:
– Interest equals “5% per 6-months”
– Interest is “12%” (12% per what?)
– Interest is 1% per month
– “Interest is “12.5% per year, compounded monthly”
• Thus, one must “decipher the various ways to state interest
Two types of interest quotation
– 1. Quotation using a Nominal Interest Rate
– 2. Quoting an Effective Periodic Interest Rate

12. Following books were used in preparation of notes
 Blank, L., Tarquin. A. 2005. Engineering Economy. 6th Edition, McGraw-Hill.
 Eschenbach, T. G. 2003. Engineering Economy”, 2nd Edition, Oxford University Press
 Riggs, J. L., Bedworth, D. D., Randhawa, S. U. 1996. Engineering Economics”, 4th Edition, Tata McGraw-Hill.
 Riggs, J. L., West. T. M. 1986. Essentials of Engineering Economics”, 2nd Edition, McGraw-Hill.
 Peter, M. S., Timmerhaus, K. D. 1991. Plant Design and Economics for Chemical Engineers. 4th Edition, McGraw-Hill.