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Comparing Quantities

    Applications of Compound Interest Formula

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8th class > Comparing Quantities > Applications of Compound Interest Formula

Applications of Compound Interest Formula

There are some situations where we could use the formula for calculation of amount in CI.

Here are a few:

(i) Increase (or decrease) in population.

(ii) The growth of a bacteria if the rate of growth is known.

(iii) The value of an item, if its price increases or decreases in the intermediate years.

Example 9: The population of a city was 20,000 in the year 1997. It increased at the rate of 5% p.a. Find the population at the end of the year 2000.

Solution:

20000 (we treat this as the principal for the 1st year)

  • Increase at 5% = 5100×20000 =
  • Population in 1999 = 20000 + = (Treat as the Principal for the 2nd year )
  • Population in 2000 = + = (Treat as the Principal for the 3rd year)
  • At the end of 2000 the population = + =

So, at the end of the year 2000, the population is approximately =

Aruna asked what is to be done if there is a decrease. The teacher then considered the following example.

Example 10: A TV was bought at a price of Rs. 21,000. After one year the value of the TV was depreciated by 5% (Depreciation means reduction of value due to use and age of the item). Find the value of the TV after one year.

Solution:

Find value of TV

  • TV was bought at a price of Rs. 21,000.
  • Reduction = 5% of ₹ per year
  • Hence, reduction = ₹
  • Value at the end of 1 year = ₹ – ₹ = ₹
  • We have found the answer.

Try these

1.A machinery worth Rs. 10,500 depreciated by 5%. Find its value after one year.

To find the value of a machinery after depreciation, we can use the formula for depreciation:

The formula is: V = P ×

Where: P is the initial value of the machinery (Rs. 10,500),

r is the rate of depreciation (5%),

V is the value after depreciation

t is the number of years

Substitute the values into the formula:

V = × 1−5100

= 10500 × (1 - ) = = 10500 × =

So, the value of the machinery after one year will be Rs. 9,975.

2.Find the population of a city after 2 years, which is at present 12 lakh, if the rate of increase is 4 %.

To find the population of a city after 2 years given a 4% annual rate of increase, we can use the formula for compound interest, as population growth in this context follows the same principle.

The formula is: P = P0 ×

Where: P0 is the present population (12 lakh = ),

r is the rate of increase ( %),

t is the time in years ( years),

P is the population after t years.

P = 1200000 × 1+41002 = 1200000 ×

= 1200000 × =

So, the population after 2 years will be approximately 12,97,920.