Question 1119011: A company invests 10,000 today to be repaid in five years in one lump sum at 12% compounded annually. If the rate of inflation is 3% compounded annually, how much profit in present day is realized over five years?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the composite rate will be 1.12 / 1.03, if i remember correctly.
your money is earning at 12% per year, but the price of goods and services you can buy with it is increasing by 3% per year.
consequently, the value of your money, in terms of what it can buy today, is increasing at the composite rate of 1.12 / 1.03 = (1.087378641 - 1) * 100% = 8.7378641% per years.
your 10,000 invested at 12% per year for 5 years would be worth 10,000 * 1.12^5 = 17,623.41683 in 5 years, if you don't take into account inflation.
with inflation, your 10,000 invested at 12% per year for 5 years would be worth 10,000 * 1.12^5 / 1.03^5 = 15,202.11417 in 5 years in terms of today's purchasing power.
how does this work?
you have 10,000 and it can buy 10,000 worth of goods and services today.
the purchasing power of your 10,000 today is 10,000 / 10,000 = 1 times as much as it is today.
you invest your money at 12% per year for 5 years.
it is worth 10,000 * 1.12 ^ 5 = 17623.41683 in 5 years.
if you buy the same amount of goods and services and the price of them didn't change, then you could buy 17623.41683 / 10,000 = 1.762341683 times the amount of goods and services as you could buy today.
however, because of inflation, the price of the goods and services increased by 3% per year.
the price 5 years from now is 10,000 * 1.03^5 = 11592.74074 dollars.
when you buy the same amount of goods and services in 5 years, you can buy 17623.41683 / 11592.74074 = 1.520211417 times the amount of goods and services as you could buy today.
your increase in purchasing power, in terms of today's dollars is equal to 1.12 ^ 5 / 1.03 ^ 5 = 1.520211417 as much as it is today.
1.12^5 / 1.03^5 is equal to (1.12/1.03)^5 which is equal to the composite rate of 1.087378641 ^ 5.
bottom line:
your composite investment rate is equal to the pure investment rate divided by the inflation rate.
in your problem, the future purchasing power of your money, in today's dollars, is equal to 10,000 * (1.12/1.03)^5 = 15,202.11417.
your profit is equal to (15,202.11417 - 10,000) / 10,000 = .520211417, or 52.02% rounded to 2 decimal places.
to find the composite interest rate per year, you take 1 plus the investment rate and divide it by 1 plus the inflation rate.
1.12 / 1.03 = 1.087378641 which is a composite rate of 8.7378641% per year, taking into account inflation.
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