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Inflation

This document discusses inflation and how it affects the value of money over time. It provides formulas to calculate future values adjusted for inflation, including the combined "interest-inflation rate" of return. Examples are given to show how to use the formulas to determine the future value of investments given interest rates and inflation rates. Practice problems at the end apply the concepts to calculate future values, selling prices adjusted for inflation, and the purchase price of an annuity.

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Eduard Lachica
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594 views6 pages

Inflation

This document discusses inflation and how it affects the value of money over time. It provides formulas to calculate future values adjusted for inflation, including the combined "interest-inflation rate" of return. Examples are given to show how to use the formulas to determine the future value of investments given interest rates and inflation rates. Practice problems at the end apply the concepts to calculate future values, selling prices adjusted for inflation, and the purchase price of an annuity.

Uploaded by

Eduard Lachica
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PPTX, PDF, TXT or read online on Scribd
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ENGINEERING ECONOMY

INFLATION
INFLATION – is the increase in the price of goods and services from one year
to another, thus decreasing the buying power of money.
𝑛
𝐹 = 𝑃 (1+ 𝑓 )

EXAMLPLE:
1. Assuming an average inflation rate of 6% during the next 5 years, how
much approximately would a car costing $400,000 now cost 5 years hence?
2. Ten years ago, an item cost $2,500. the rate of inflation for the first 4 years
was 4%, during the next 3 years, 6% and for the last years, 9%. Assuming that
the increase in price were due to inflation alone, what is the average inflation
rate during the 10 years?
VALUE OF MONEY IN TERMS OF CURRENT BUYING
POWER
𝑛
′ 𝑃 (1+ 𝑖 )
𝑃= 𝑛
( 1+ 𝑓 )
′
𝑃 =𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑚𝑜𝑛𝑒𝑦 𝑖𝑛 𝑡𝑒𝑟𝑚𝑠 𝑜𝑓 𝑡h𝑒𝑐𝑢𝑟𝑟𝑒𝑛𝑡 ( 𝑦𝑒𝑎𝑟 0 ) 𝑏𝑢𝑦𝑖𝑛𝑔 𝑝𝑜𝑤𝑒𝑟
𝑖=𝑎𝑛𝑛𝑢𝑎𝑙 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝑓 =𝑎𝑛𝑛𝑢𝑎𝑙 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑟𝑎𝑡𝑒

EXAMPLE :
A company invest $10,000 today to be repaid in 5 years in one lump sum at
12% compounded annually. If the rate of inflation is 3% compounded annually,
how much profit in the present day dollar, is realized over the 5 years?
𝑛 5
′ 𝑃 (1+ 𝑖 ) 10000 ( 1+12 % )
𝑃= 𝑛
→= 5
= $ 𝟏𝟓 , 𝟐𝟎𝟐 . 𝟏𝟏
( 1+ 𝑓 ) ( 1+3 % )

𝑝𝑟𝑜𝑓𝑖𝑡 𝑖𝑛𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑑𝑎𝑦 𝑑𝑜𝑙𝑙𝑜𝑟=$ 15,202.11− % $ 10,000=$ 𝟓 ,𝟐𝟎𝟐 .𝟏𝟏


COMBINED “INTEREST-INFLATION RATE” OF RETURN
𝑛
𝐹 = 𝑃 ( 1+𝑖𝑐 )
𝑖𝑐 =𝑖+ 𝑓 +𝑖𝑓

𝑖𝑐 =𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 − 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛


𝑖=𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝑓 =𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒

EXAMPLE:
What is the uninflated present worth of $2000 in 2 years if inflation rate is 6%
and standard interest rate is 10%?
𝑖𝑐 =𝑖+ 𝑓 +𝑖𝑓 → 0.10+ 0.06+ 0.10 ( 0.06 ) =𝟎 . 𝟏𝟔𝟔

𝐹 = 𝑃 ( 1+𝑖𝑐 ) 𝑛 → 𝑃 = 𝐹 ( 1+𝑖 𝑐 ) −𝑛

𝑃=2000 ( 1.166 )− 2= $ 𝟏𝟒𝟕𝟏


PRACTICE PROBLEM
1. 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 dollar, after 5 years
if inflation rate remains the same at the rate of 8% per year? $10,960.86
2. One economist has predicted that there will be a 7% per year inflation rate of
prices during the next 10 years. If proves to be correct, an item that presently sells
for $100 would sell for what price 10 years hence? $196.67
3. An engineer has received $10,000 from his employer for the patent disclosure. He
has decided to invest the money in a 15 year savings certificate that pays 8% per
year, compounded annually. What will be the final value of his investment, in terms
of today’s dollars, if the inflation continues at the rate of 6% per year? $13,236.35
4. An engineer is considering the purchase of an annuity that will pay $1000 per year
for 10 years. The engineer feels he should obtain a 5% rate of return on the annuity
after considering the effect of an estimated 6% inflation rate per year. The amount he
would be willing to pay to purchase the annuity is __________? $5815.88

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