ENGINEERING ECONOMICS
Simple Interest
The capital originally invested in a
transaction is called the principal (p). At
any time after the investment of the
principal, the sum of the principal and the
interest due is called the amount (F).
𝑭=𝑷+𝑰
𝑰 = 𝑷𝒓𝒕
Exact interest for t days.
𝑰 = 𝑷𝒓
𝒕
𝟑𝟔𝟓
Ordinary interest for t days.
𝑰 = 𝑷𝒓
𝒕
𝟑𝟔𝟎
Simple discount:
𝐼=𝐹𝑑𝑡
Interest:
The amount of money paid for the use of
money called the capital for a certain period
of time.
Simple Interest:
The interest to be paid which is proportional
to the length of time the principal is used.
Principal:
The amount of money used on which interest
is charge.
Rate of interest:
The amount earned by one unit of principal
during a unit of time.
𝐼 = 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝐹 = 𝑎𝑚𝑜𝑢𝑛𝑡 𝑑𝑢𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑒𝑛𝑑 𝑜𝑓 𝑡𝑖𝑚𝑒 "𝑡"
𝑑 = 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑟𝑎𝑡𝑒
𝑃+𝐼 =𝐹
𝑃 =𝐹−𝐼
𝑃 = 𝐹 − 𝐹 𝑑𝑡
Ordinary interest:
An interest based on the exact number of
one banker’s year which is equal to 12
months.
One month
One year
=
=
30 days
360 days
𝑃 = 𝐹(1 − 𝑑𝑡)
Banker’s discount:
𝒊=
𝒅
𝟏−𝒅
Exact interest:
An interest based on the exact number of
days, 365 days for ordinary year and 366
days for leap year.
FORMULA FOR SIMPLE INTEREST
Compound Interest
I = P rt
I = interest
P = principal
i = rate of interest in decimal
The interest earned by the principal which is
added to the principal will also earn an
interest for the succeeding periods.
n = number of interest periods
F = total amount
F=P+1
F = P (1 + rt)
When t = 1 (after one year)
F= P (1 + r)
𝐹 = 𝑃(1 + 𝑖)𝑛
P = present worth or principal
F = compound amount at the end of “n”
periods
Discount:
i = rate of interest
Is the difference between the future worth
and its present worth.
n = no. of periods
Rate of discount:
(1 + 𝑖)𝑛 = Single Payment Compound
Amount Factor
The discount on one unit of principal per
unit of time
d = rate of discount
d = F – 𝑃1
𝑖
d = 1+𝑖 (𝑟𝑎𝑡𝑒 𝑜𝑓 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡)
Equivalent Rate of Interest
𝑑=
𝑖
(1 + 𝑖)
𝑑 + 𝑑𝑖 = 𝑖
𝑖 − 𝑑𝑖 = 𝑑
𝑖(1 − 𝑑) = 𝑑
𝑖=
𝑑
(𝑟𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡)
1−𝑑
1. For 8% compounded annually for 5
years
i = 0.08
n = 5 periods
2. For 8% compounded semi-annually
for 5 years
0.08
i = 2 = 0.04 ; n = 5(2) = 10
3. For 8% compounded quarterly for 5
years
i=
0.08
4
= 0.02 ; n = 5(4) = 20
4. For 8% compounded monthly for 5
years
i=
0.08
12
= 0.00667 ; n = 5(12) = 60
5. For 8% compounded bi-monthly for
5 years
0.08
i = 6 = 0.013 ; n = 5(6) = 30
Continuous Compounding
𝑭𝒐𝒓𝒎𝒖𝒍𝒂𝒔:
1. Present Worth
𝑃=
𝐹
𝑒 𝑟𝑛
𝑃 = 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑤𝑜𝑟𝑡ℎ
𝐹 = 𝑓𝑢𝑡𝑢𝑟𝑒 𝑤𝑜𝑟𝑡ℎ
𝑟 =
𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝑛 = 𝑛𝑜. 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑𝑠
2. 𝐹𝑢𝑡𝑢𝑟𝑒 𝑤𝑜𝑟𝑡ℎ:
𝐹 = 𝑃 𝑒 𝑟𝑛
3. 𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑎𝑚𝑜𝑢𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟:
𝑒 𝑟𝑛 = 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑎𝑚𝑜𝑢𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟
4. 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑤𝑜𝑟𝑡ℎ 𝑓𝑎𝑐𝑡𝑜𝑟:
1
= 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑤𝑜𝑟𝑡ℎ 𝑓𝑎𝑐𝑡𝑜𝑟
𝑒 𝑟𝑛
5. 𝑬𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆 𝒂𝒏𝒏𝒖𝒂𝒍 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕:
𝑖𝑒 = 𝑒 𝑟 − 1
𝑖𝑒 = 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑎𝑛𝑛𝑢𝑎𝑙 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝑟 = 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑒𝑑 𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑠𝑙𝑦