ENGINEERING ECONOMICS
Discounts & Inflation
DISCOUNTS
Discount - is interest paid in advance.
Discount = Future worth – Present worth
𝒅 = 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 / principal
d = discount rate
𝑑
i=
1−𝑑
i = interest rate
Where:
d = rate of discount for the period involved
i = rate of interest for the same period
Sample Problem 1
• A man borrowed 5,000 from a bank and
agreed to pay the loan at the end of 9 months.
The bank discounted the loan and gave him
4,000 in cash.
a. what was the rate of discount?
b. What was the rate of interest?
c. What was the rate of interest for one year?
Solution:
Solution:
a.
𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡
1,000
𝑑=
=
= 0.20 𝑜𝑟 20%
𝑝𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙
5000
a. what was the rate of
discount?
b.
𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡
0.20
i=
=
= 0.25 𝑜𝑟 25%
1 − 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡
1 − 0.20
b. What was the rate of
interest?
c.
I = 𝑃𝑛𝑖
c. What was the rate of interest for one year?
I=I/Pn
(1000)/(5000)(9/12)
=0.2667= 26.67%
INFLATION
Inflation is the increase on the
prices for goods and services from
one year to another, thus decreasing
the purchasing power of money.
n
𝐹𝐶 = 𝑃𝐶 (1 + 𝑓)
where:
PC = present cost of commodity
FC = future cost of the same commodity
f = annual inflation rate
n = number of years
Sample Problem 2
• An item presently costs 1,000. If
inflation is at the rate of 8% per year,
what will be the cost of the item in
two years?
Solution:
An item presently costs 1,000. If
inflation is at the rate of 8% per
year, what will be the cost of the
item in two years?
Given:
PC
f
n
FC
= P 1,000
= 8%
= 2 yrs
=?
FC = PC (1+f)n = P1,000 (1+0.08)2 = P1,166.4
In an inflationary economy, the buying power
of money decreases as costs increases. Thus,
𝑃
𝐹=
1+𝑓 𝑛
Where:
F is the future worth measured in today’s
pesos of a present amount P
Sample Problem 3
• An economy is experiencing inflation at an
annual rate of 8%. If this continues, what
will 1,000 be worth two years from now?
Solution:
Solution:
Given:
P
f
n
An economy is experiencing inflation at
an annual rate of 8%. If this continues,
what will 1,000 be worth two years
from now?
= P 1,000
= 8%
= 2 yrs
𝐹=
𝑃
1,000
𝑛 = =
2 = P 857.34
1+𝑓
1+0.08
If interest is being compounded at the
same time that inflation is occurring,
the future worth will be:
1+𝑖 n
𝐹 = 𝑃( )
1+𝑓
Sample Problem 4
A man invested 10,000 at an interest rate of 10%
compounded annually. What will be the final
amount of his investment in terms of today’s
pesos, after 5 years if inflation remains the same
at the rate of 8% per year.
Solution:
Solution:
Given:
P
i
f
n
= P 10,000
= 10%
= 8%
= 5 yrs
A man invested 10,000 at an
interest rate of 10% compounded
annually. What will be the final
amount of his investment in terms
of today’s pesos, after 5 years if
inflation remains the same at the
rate of 8% per year.
1+𝑖 n
𝐹 = 𝑃( )
1+𝑓
F = P 10, 960.86
Thank you!!!